EP2192577A1 - Optimization of MP3 encoding with complete decoder compatibility - Google Patents
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Definitions
- Example embodiments herein relate to audio signal encoding, and in particular to rate-distortion optimization for MP3 encoding.
- MP3 MPEG I/II Layer-3
- An example MP3 encoder is LAME, which refers to "LAME Ain't an Mp3 Encoder", as is known in the art.
- Another MP3 encoder is ISO reference codec, which is based on the ISO standard.
- MP3 encoders include use of two nested loop search (TNLS) algorithms, which are computationally complex and may not be guaranteed to converge. These encoders may be configured or operated to provide for additional functionality and customization.
- TNLS nested loop search
- the encoding algorithm is not standardized in MP3, the basic structure and syntax-related tools are fixed so that the MP3 encoded/compressed bitstreams can be correctly decoded by any standard compatible decoder. However, there may be opportunities to manipulate the encoding algorithm while maintaining full decoder compatibility.
- Figure 1 shows an MP3 encoding process to which example embodiments may be applied
- Figure 2 shows a flow diagram of an optimization process in accordance with an example embodiment
- Figure 3 shows a graph of an optimal path search algorithm for use in the process of Figure 2 ;
- Figure 4 shows the graph of Figure 3 , illustrating an optimal path
- Figure 5 shows a flow diagram of a process to be used in the optimization process of Figure 2 ;
- Figure 6 shows a graph of performance characteristics of an example embodiment, for encoding of audio file waltz.wav as compared to ISO reference codec;
- Figure 7 shows a graph of performance characteristics of an example embodiment, for encoding of audio file waltz.wav as compared to LAME;
- Figure 8 shows a graph of performance characteristics of an example embodiment, for encoding of audio file vioin.wav as compared to ISO reference codec;
- Figure 9 shows a graph of performance characteristics of an example embodiment, for encoding of audio file violin.wav as compared to LAME.
- Figure 10 shows an encoder for optimizing encoding performance of MP3 in accordance with an example embodiment.
- the present application provides a method for optimizing audio encoding of a source sequence, the encoding being dependent on quantization factors, the quantization factors including a global quantization step size and scale factors.
- the method includes defining a cost function of the encoding of the source sequence, the cost function being dependent on the quantization factors.
- the method includes initializing fixed values of the scale factors; and determining values of the quantization factors which minimize the cost function by iteratively performing:
- the present application provides an encoder for optimizing audio encoding of a source sequence, the audio encoding being dependent on quantization factors, the quantization factors including a global quantization step size and scale factors.
- the encoder includes a controller, a memory accessible by the controller, a cost function of an encoding of the source sequence stored in memory, the cost function being dependent on the quantization factors; and a predetermined threshold of the cost function stored in the memory.
- the controller is configured to access the cost function and predetermined threshold from memory, initialize fixed values of the scale factors, and determine values of the quantization factors which minimize the cost function by iteratively performing:
- FIG. 1 shows an MP3 encoding process 20 to which example embodiments may be applied.
- the MP3 encoding process 20 receives digital audio input 22 and produces a compressed or encoded output 32 in the form of a bitstream for storage and transmission.
- the encoding process 20 may for example be implemented by an encoder such as a suitably configured computing device.
- continuous lines denote the time or spectral domain signal flow, and dash lines denote the control information flow.
- the encoding process 20 includes audio input 22 for input to a time/frequency (T/F) mapping module 24 and a psychoacoustic model module 26.
- a quantization and entropy coding module 28 and a frame packing module 30 are also shown.
- the encoding process 20 results in an encoded output 32 of the audio input 22, for example for sending to a decoder for subsequent decoding.
- the audio input 22 (in time domain) are first input into the T/F mapping module 24, which converts the audio input 22 into spectral coefficients.
- the T/F mapping module 24 is composed of three steps: pseudo-quadrature mirror filter (PQMF), windowing and modified discrete cosine transform (MDCT), and aliasing reduction.
- PQMF pseudo-quadrature mirror filter
- MDCT modified discrete cosine transform
- aliasing reduction aliasing reduction.
- the PQMF filterbank splits a so-called granule (in MPEG I and II layer 3 each audio frame contains 2 and 1 granules respectively) of 576 input audio samples into 32 equally spaced subbands, where each subband has 18 time domain audio samples.
- the 18 time domain audio samples in each subband are then combined with their counterpart of the next frame, and processed by a sine-type window based on psychoacoustic modeling decisions.
- a long window which covers a whole length of 36, addresses stationary audio parts.
- Long windowing with MDCT afterwards ensures a high frequency resolution, but also causes quantization errors spreading over the 1152 time-samples in the process of quantization.
- a short window is used to reduce the temporal noise to spread for the signals containing transients/attacks.
- audio signals with a length of 36 are divided into 3 equal sub-blocks.
- two transition windows, long-short (start) and short-long (stop), which have the same size as a long window are employed.
- the psychoacoustic model module 26 is generally used to generate control information for the T/F mapping module 24, and for the quantization and entropy coding module 28. Based on the control information from the psychoacoustic model module 26, the spectral coefficients which are output from the T/F mapping module 24 are received by the quantization and entropy coding module 28, and are quantized and entropy coded. Finally these compressed bits streams are packed up along with format information, control information and other auxiliary data in MP3 frames, and output as the encoded output 32.
- the MP3 syntax leaves the selection of quantization step sizes and Huffman codebooks to each encoder or encoding algorithm, which provides opportunity to apply rate-distortion consideration.
- a conventional MP3 encoding algorithm is now be described as follows, which employs a "hard decision quantization", a two nested loop search (TNLS) algorithm, and fixed or static Huffman codebooks.
- the MP3 quantization and entropy coding module 28 first subdivides an entire frame of 576 spectral coefficients into 21 or 12 scale factor bands for a long window block (including long-short window and short-long window) or a short window block respectively.
- scale_factor sb 2 ⁇ scalefac sub_block ⁇ sb + preflag ⁇ pretab sb ⁇ 1 + scalefac_scale + 8 ⁇ subblock_gain sub_block .
- each of the parameters listed in (2.2) may be referred to as a "scale factor”, and all of which may be collectively referred to herein as “scale factors”, as appropriate.
- global_gain and the scale factors may collectively be referred to herein as “quantization factors”.
- sub_block is only used for short windows, and it refers to one of the 3 sub-blocks for a short window.
- scalefac[sub_block][sb] is a scale factor parameter for scale factor band sb to color the quantization noise.
- scalefac[sub_block][sb] are variable length transmitted according to scalefac_compress which occupies 4 bits (MPEG-1) or 9 bits (MPEG-2) in the side information of MP3 encoded frames.
- preflag is a shortcut for additional high frequency amplification of the quantized values. If preflag is set, the values of a fixed table pretab[sb] are added to the scale factors. preflag is never used in short windows (for the purposes of the standard).
- subblock_gain[sub_block] is the gain offset for the short window.
- scalefac-scale is a one-bit parameter used to control the quantization step size.
- the quantized spectral coefficients are then encoded by static Huffman coding, which utilizes 34 fixed Huffman codebooks.
- static Huffman coding utilizes 34 fixed Huffman codebooks.
- MP3 subdivides the entire quantized spectrum into three regions. Each region is coded with a different set of Huffman codebooks that best match the statistics of that region. Specifically, at high frequencies, MP3 identifies a region of "all zeros". The size of this region can be deduced from the sizes of the other two regions, and the coefficients in this region don't need to be coded. The only restriction is that it must contain an even number of zeros since the other two regions group their values in 2- or 4-tuples.
- the second region contains a series of contiguous values consisting only of -1, 0, +1 just before the "zero” region, and is encoded in 4-tuples by Huffman codebook 32 or 33.
- the low frequency region covers the remaining coefficients which are encoded in pairs. This region is further subdivided into 3 (for long window) or 2 (for short, long-short and short-long window) parts with each covered by a distinct Huffman codebook.
- a noise shaping method may be applied to find the proper global quantization step size global_gain and scale factors before the actual quantization.
- Some conventional algorithms use the TNLS algorithm to jointly control the bit rate and distortion.
- the TNLS algorithm consists of an inner (rate control) loop and an outer (noise control) loop.
- the task of the inner loop is to change the global quantization step size global_gain such that the given spectral data can just be encoded with the number of bits available. If the number of bits resulting from Huffman coding exceeds this number, the global_gain can be increased to result in a larger quantization step size, leading to smaller quantized values. This operation is repeated until the resulting bit demand for Huffman coding is small enough.
- the TNLS algorithm may require quantization step sizes so small to obtain the best perceptual quality. On the other hand, it has to increase to the quantization step sizes to enable coding at the required bit rate. These two requirements are conflicting. Therefore, this conventional algorithm does not guarantee to converge.
- soft decision quantization instead of the hard decision quantization, is applied, and the corresponding purpose of quantization and entropy coding in MP3 encoding is to achieve the minimum perceptual distortion for a given encoding bit rate by solving, mathematically, the following minimization problem: ⁇ min y , q , p , h D w xr ⁇ rxr , subject to R q + R y ⁇ P ⁇ H ⁇ R 1
- xr is the original spectral signal
- rxr is the reconstructed signal obtained from the quantized spectral coefficients y
- P and H represent Huffman codebook region partition and Huffman codebooks selection respectively
- q denotes the quantization factors including global_gain and scale factors
- R ( q ) and R ( y , P , H ) are the bit rates to encode q and the quantized spectral coefficients y respectively
- R 1 is the rate constraint
- y is not calculated according to (2.1) any more; instead, it is treated as a variable in a cost function involving the distortion and rates, and has to be determined jointly along with q , P , and H .
- Average noise-to mask ratio (ANMR) is used as the distortion measure.
- the noise-to mask ratio (NMR), the ratio of the quantization noise to the masking threshold, is a widely used objective measure for the evaluation of an audio signal.
- N is the number of scale factor bands
- w [sb] is the inverse of the masking threshold for scale factor band sb
- d [sb] is the quantization distortion, mean squared quantization error for scale factor band sb.
- FIG. 2 shows a flow diagram of an optimization process 50 in accordance with an example embodiment.
- the exact order of steps may vary from those shown in Figure 2 in different applications and embodiments. It can also be appreciated that more or less steps may be required in some example embodiments, as appropriate.
- the parameters y, q , P and H are jointly optimized.
- the general framework for the process 50 has been outlined previously in Xu and E.-h. Yang, "Rate-distortion optimization for MP3 audio coding with complete decoder compatibility," in Proc. 2005 IEEE Workshop on Multimedia Signal Processing, Oct. 2005 , the contents of which are herein incorporated by reference.
- the process 50 selects the quantized spectral coefficients y and Huffman codebook region division P , quantization factors q and Huffman codebook region selection H alternatively to minimize the Lagrangian cost J .
- the iterative searching for the parameters may be referred to as "soft-decision quantization” (rather than the formulaic "hard-decision quantization” of (2.1), described above).
- the iterative algorithm of the process 50 can be described as follows.
- step 52 specify a tolerance ⁇ as the convergence criterion for the Lagrangian cost J .
- q t and H t are fixed or given for any t ⁇ 0.
- y t and P t achieve the minimum min y
- P ⁇ J ⁇ D w ⁇ xr , Q - 1 q ⁇ y + ⁇ ⁇ R q t + R y ⁇ P ⁇ H t
- Q -1 ( q,y ) is used to generate the reconstructed signal rxr.
- J ⁇ ( y t , q t , P t , H t ) by J ⁇ t .
- step 60 given y t , P t and q t+1, update H t to H t+1 so that H t+1 achieves the minimum min H R ⁇ y t ⁇ P t + 1 ⁇ H t .
- the final y, q, P and H may thereafter be provided for MP3 coding of xr.
- Figure 3 shows a graph 80 of an optimal path search algorithm for use in the process of Figure 2 ; while Figure 4 shows an optimal path of the graph 80.
- the graph 80 is defined with 4 layers (shown as I, II, III, and IV) and 288 nodes in each layer as shown in Figure 3 .
- the 4 layers correspond to the three divisions of the big_value region and the count_1 region.
- Two special states, frame_begin and frame_end denote the start and end of the frame respectively.
- a cost which is defined as the minimum incremental Lagrangian cost of quantizing and Huffman encoding the coefficients of state S L,i (or states S Li-1 and S L,i if L IV ) by using the Huffman codebook selected for layer L.
- every sequence of connections from the frame_begin state to the frame_end state corresponds to a Huffman codebook region division of the entire frame with a Lagrangian cost.
- the sequence of connection in Figure 4 assigns scale factor band 0 and 1 to the fist two subdivisions of the big_value region respectively, the next 4 coefficients to the count_ 1 region, and the rest to the zero region.
- any Huffman codebook region division of the entire frame that is compatible with the standard can be represented by a sequence of connections from the frame_begin to the frame_end state in the graph 80.
- the algorithm preselects and stores the best quantized coefficients based on minimizing the Lagrangian cost of (3.7) for each legitimate state S L,i , and sets their associated cost as the cost of each connection to that state.
- the algorithm also recursively precalculates, for each state, the distortion/cost resulting from ending the frame at that state, i.e., the cost of its connection to the state frame_end.
- the algorithm begins with the state frame_begin by storing the cost of dropping the entire frame in J frame_begin.
- the cost of each state is set to the cost of corresponding incoming connection, and added with the cost of dropping the remaining coefficients to get J I,0 and J IV,0 , respectively.
- only states S L,1 has an incoming connection from states S I,0 .
- Set its cost to the sum of the costs of state S I,0 and the connection between S I,0 and S I,1, and add it with the cost of dropping the remaining coefficients to get J I,1.
- a three-layer graph could be constructed for other three window cases.
- Step 58 generally determines the quantization factors q (i.e., scale factors and global_gain) that minimize the combined cost of weighted distortion and bit rate for encoding or transmittal. Given the nonuniform quantizer and nonlinear bit rate for quantization factors in the standard, there is no direct formula to calculate the optimal quantization factors. Direct search through all combinations of global_gain, scalefac_compress, scalefac, scalfac_scale , and subblock_gain (for short windows) or preflag (for other windows) may be computationally complex.
- q i.e., scale factors and global_gain
- the method 100 includes the following alternating minimization procedure to minimize the combined cost.
- global_gain is determined while the scale factors are fixed, and at step 104 the scale factors are determined while global_gain is fixed. This is repeated iteratively until the calculated rate-distortion cost is within a predetermined threshold.
- step 102 update global_gain when scalefac, scalfac_scale and subblock _gain (for short windows) or preflag (for other windows) are fixed.
- the bit rate for the transmission of scale factors is fixed. Therefore, at this stage only the encoding distortion is minimized, while rate is not considered.
- s[sb] global_gain-210-scale_factor[sb]
- I[sb] and l[sb+1]-1 are the start and end positions for scale factor band sb respectively
- w[sb] is the inverse of the masking threshold for scale factor band sb.
- step 104 fix global_gain. Update the scale factors scalefac, scalfac_scale and subblock_gain (for short windows) or preflag (for other windows) to minimize the combined cost of weighted distortion and bit rate for transmitting the scale factors.
- preflag is equal to 0 or 1.
- the value of pretab[sb] is typically fixed and is of the form as shown in Table 1.
- scalefac_scale is equal to 0 or 1.
- scalefac_compress determines the number of bits used for the transmission of the scalefactors according to Table 2.
- bit length may be a first bit length for a first group of scale factor bands and the bit length may be a second bit length for a second group of scale factor bands.
- slen1 is the bit length of scalefac for each of scalefactor bands 0 to 10
- slen2 is the bit length of scalefac for each of scalefactor bands 11 to 20.
- the maximum length for slen1 is 4 while the maximum length for slen2 is 3 (as based on the MP3 standard).
- slen1 and s len2 are given, in some example embodiments, one can find the minimum encoding distortion for each scalefactor band and the corresponding scalefac[sb] which generates the minimum encoding distortion.
- preflag and scalfac_scale are fixed, there only needs to be calculated 5 (the first 11 bands) or 4 (the last 10 bands) different cases of encoding distortion for each scale factor band, rather than calculate the encoding distortion 16 times for different scalefac_compress.
- the pre-calculated encoding distortion is minimized with a certain value for scalefac[sb] given the length slen1 or slen2.
- sf[sb][slen] as the value for scalefac[sb] such that the weighted distortion is minimized for scale factor band sb when the bit length used for transmitting scalefac[sb] is slen.
- s[sb] in equation (3.9) can be freely chosen. That is, s[sb] is not restricted by the value of scalefac[sb] to be one of the 16 integer numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15). Apply the minimum mean square error criterion to find the minimum weighted distortion for (3.9).
- scalefac[sb] s[sb]+210
- the corresponding value for scalefac[sb] is (global_gain - sg[sb]) / 2 (1+sCaifac_scale) - preflag ⁇ pretab[sb].
- T scalefac[sb] cannot be freely chosen in reality (as defined by the standard), that is, it must be constrained to one of the 16 integer numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15).
- the value of scalefac[sb] can be determined using the following algorithm.
- each scale factor band there exists one redundant case for each scale factor band if scalefac[sb] is equal to 0 (i.e., (3.16) may be calculated once). As a result, in some example embodiments, there are 9 (the first 11 scale factor bands) or 15 (the last 10 scale factor bands) different cases of encoding distortion for each scale factor band.
- the total Lagrangian cost is the addition of the encoding distortion and the bit rate. Therefore, what remains is the addition of bit rate to calculate the combined cost.
- the distortion based on bit rate for the transmission of all scale factors can also be looked up from a pre-generated table, as is known in the art. Similarly, for other window cases, a similar approach could be applied to reduce the computational complexity.
- step 106 repeat steps 102 and 104 until the decrease of the combined cost is below a prescribed threshold. If the predetermined threshold is reached, at step 110 output the final global_gain and scale factors ( scalefac, scalfac_scale, preflaglsubblock_gain ) , and then ends at step 112 (or proceed to the next step in method 50 ( Figure 2 )).
- the iterative method 100 generally converges after two rounds of iteration, the number of different cases to be computed for each scale factor band of an MPEG-1 encoded, long-window frame has been reduced from 16384 to 18 (the first 11 bands) or 30 (the last 10 bands).
- the particular quantization factors or scale factors to be determined may depend on the particular application or coding scheme, and may not be limited to the parameters global_gain, scalefac, scalfac_scale, and preflag / subblock_gain.
- determining the Huffman codebook H may be performed as follows: for each region, every Huffman codebook that has encodable value limit larger than or equal to the greatest coefficient amplitude of that region is considered, and the one with the minimum codeword length is selected.
- PE Perceptual Entropy of an encoded frame
- R is the encoding bit rate
- M is the number of audio samples to be encoded.
- c 1 , c 2 and c 3 are determined from the experimental data using the least square criterion. This is for example generally described in C.
- X represents independent variables PE and R.
- y represents the dependent variable ⁇ final R .
- fun represents the formula (4.1).
- beta0 is a vector containing initial values for the coefficients for c 1 , c 2 and c 3 .
- the average number of iterations was tested over the Lagrangian multiplier if the formula (4.1) with the above estimated coefficient is used as the initial point for the bisection search.
- the average number of iterations over the Lagrangian multiplier is 1.5.
- the average number of iterations over the Lagrangian multiplier ranges from 4 to 8 if an arbitrary number is used as the initial point. Therefore, on the average, using (4.1) as the initial point can run 4 times as fast as the method in which an arbitrary initial point is used.
- Figure 6 shows a graph 140 of performance characteristics of an example embodiment, showing a comparison of the method 50 (Figure 20) for encoding of audio file waltz.wav as compared to ISO reference codec.
- Figure 7 shows a graph 150 of performance characteristics of an example embodiment, for encoding of audio file waltz.wav as compared to LAME.
- Figure 8 shows a graph 160 of performance characteristics of an example embodiment, for encoding of audio file vioin.wav as compared to ISO reference codec.
- Figure 9 shows a graph 170 of performance characteristics of an example embodiment, for encoding of audio file violin.wav as compared to LAME.
- the LAME MP3 encoder features a psychoacoustic model, joint stereo encoding and variable bit-rate encoding.
- LAME still uses the basic structure of typical TNLS.
- a refining TNLS is used to minimize the total noise to masking ratio for an entire frame after the successful termination of search process given its typical TNLS. Specifically, during each outer loop, the band with maximum noise to masking ratio is amplified and the best result based on total noise to mask ratio is stored.
- the method 50 ( Figure 2 ) is implemented as described above. For each case, the perceptual model, joint stereo encoding mode and window switching decision are kept intact.
- Figure 6 shows the rate-distortion performance of the method 50 ( Figure 2 ) (denoted as "RD optimization" in the graph 140) applied to ISO reference encoder, when compared to a conventional or normal ISO reference encoder implementing TNLS, in constant bit-rate mode for waltz.wav.
- the test file may for example be encoded at 48khz, 2 channel, 16 bits/sample, 30 seconds.
- ISO-HO represents the optimal Huffman tables used for Huffman coding
- ISO-NH means that the first Huffman table satisfying the coding limit is selected for each Huffman coding region.
- the vertical axes denote the average noise to mask ratio over all audio frames.
- Figure 7 depicts the rate-distortion performance of the method 50 ( Figure 2 ) (also denoted as "RD optimization) applied to LAME when compared to the LAME reference encoder (implementing conventional TNLS) in constant bit-rate mode for waltz.wav. It is shown separately from ISO reference encoder because ISO reference encoder and LAME adopt different perceptual models. For an unbiased comparison, in some example embodiments the LAME encoder disables the functions of amplitude scaling and low pass filter. In Figure 7 , “LAME” means that the audio file is compressed using LAME's normal compression mode. As shown, the method 50 ( Figure 2 ) outperforms LAME in terms of compression performance. At 96kbps, the proposed optimization algorithm achieves about 1.34dB ANMR gain over LAME.
- Figures 8 and 9 compare the compression performance of the method 50 ( Figure 2 ) for the music file violin.wav (MPEG lossless audio coding test file, 48khz, 2 channel, 16 bits/sample, 30 seconds) in constant bit-rate mode.
- Figure 8 shows results from ISO reference encoder
- Figure 9 shows results from LAME. It may be observed that "RD optimization" has improved rate-distortion over the conventional reference encoders. Similar results may be observed for other test music files.
- Step 56 the search range for y j is set to [yh j -a, yh j +a], where yh j is the jth quantized coefficient from hard decision quantization (e.g.
- y j is determined from (2.1)) and a is a fixed integer.
- a is a fixed integer.
- the average number of iterations over the Lagrangian multiplier is 1.5 if the formula (4.1) is used as the initial point.
- the average number of iterations over the Lagrangian multiplier ranges from 4 to 8 if an arbitrary number is used as the initial point.
- Table 3 lists the computation time (in seconds) on a Pentium PC, 2.16GHZ, 1G by tes of RAM to encode violin.wav and waltz.wav at different transmission rates for the method 50 based on LAME reference codec.
- the proposed optimization algorithm generally reaches real time throughput, which suggests that the method 50 is computationally efficient.
- the computation time is generally less than 30 seconds.
- the computation time for ISO-based encoders is not listed, but are generally less-efficient than LAME-based encoders in both the computation time and compression performance.
- the encoder 300 may for example be implemented on a suitable configured computer device.
- the encoder 300 includes a controller such as a microprocessor 304 that controls the overall operation of the encoder 300.
- the microprocessor 304 may also interact with other subsystems (not shown) such as a communications subsystem, display, and one or more auxiliary input/output (I/O) subsystems or devices.
- the encoder 300 includes a memory 304 accessible by the microprocessor 304. Operating system software 306 and various software applications 308 used by the microprocessor 302 are, in some example embodiments, stored in memory 304 or similar storage element.
- MP3 software application 310 such as the ISO-based encoder or LAME-based encoder described above, may be installed as one of the various software applications 308.
- the microprocessor 302 in addition to its operating system functions, in example embodiments enables execution of software applications 308 on the device.
- the encoder 300 may be used for optimizing performance of MP3 encoding of a source sequence. Specifically, the encoder 300 may enable the microprocessor 304 to determine quantization factors (for example including a global quantization step size and scale factors) for the source sequence.
- the memory 304 may contain a cost function of an encoding of the source sequence, wherein the cost function is dependent on the quantization factors.
- the memory 304 may also contain a predetermined tolerance of the cost function stored in the memory 304. Instructions residing in memory 304 enable the microprocessor 203 to access the cost function and predetermined tolerance from memory 304, determine the quantization factors which minimize the cost function within the predetermined tolerance, and store the determined quantization factors in memory 304 for MP3 encoding of the source sequence.
- an iterative method is performed such that global_gain is determined while the scale factors are fixed, and the scale factors are determined while g / obal_gain is fixed. This is repeated until a calculated rate-distortion cost is within a predetermined threshold.
- the MP3 software application 310 may be used to perform MP3 encoding using the determined quantization factors.
- the encoder 300 may be configured for optimizing of parameters including quantization factors, in a manner similar to the example methods described above.
- the encoder 300 may be configured to perform the method 50 ( Figure 2 ).
- example embodiments may be adapted to or implemented by other forms of signal encoding or audio signal encoding, for example Advanced Audio Coding.
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- Compression Or Coding Systems Of Tv Signals (AREA)
Abstract
Description
- Example embodiments herein relate to audio signal encoding, and in particular to rate-distortion optimization for MP3 encoding.
- Many compression standards have been developed and evolved for the efficient use of storage and/or transmission resources. Among these standards is the audio coding scheme MPEG I/II Layer-3 (conventionally referred to as "MP3"), which has been a popular audio coding method since its inception in 1991. MP3 has greatly facilitated the storage and access of audio files. MP3 is now widely used in the Internet, portable audio devices and wireless communications.
- An example MP3 encoder is LAME, which refers to "LAME Ain't an Mp3 Encoder", as is known in the art. Another MP3 encoder is ISO reference codec, which is based on the ISO standard. Generally, such MP3 encoders include use of two nested loop search (TNLS) algorithms, which are computationally complex and may not be guaranteed to converge. These encoders may be configured or operated to provide for additional functionality and customization.
- Generally, although the encoding algorithm is not standardized in MP3, the basic structure and syntax-related tools are fixed so that the MP3 encoded/compressed bitstreams can be correctly decoded by any standard compatible decoder. However, there may be opportunities to manipulate the encoding algorithm while maintaining full decoder compatibility.
- Reference will now be made, by way of example, to the accompanying drawings which show example embodiments of the present application, and in which:
-
Figure 1 shows an MP3 encoding process to which example embodiments may be applied; -
Figure 2 shows a flow diagram of an optimization process in accordance with an example embodiment; -
Figure 3 shows a graph of an optimal path search algorithm for use in the process ofFigure 2 ; -
Figure 4 shows the graph ofFigure 3 , illustrating an optimal path; -
Figure 5 shows a flow diagram of a process to be used in the optimization process ofFigure 2 ; -
Figure 6 shows a graph of performance characteristics of an example embodiment, for encoding of audio file waltz.wav as compared to ISO reference codec; -
Figure 7 shows a graph of performance characteristics of an example embodiment, for encoding of audio file waltz.wav as compared to LAME; -
Figure 8 shows a graph of performance characteristics of an example embodiment, for encoding of audio file vioin.wav as compared to ISO reference codec; -
Figure 9 shows a graph of performance characteristics of an example embodiment, for encoding of audio file violin.wav as compared to LAME; and -
Figure 10 shows an encoder for optimizing encoding performance of MP3 in accordance with an example embodiment. - It would be advantageous to provide an iterative optimization algorithm to jointly optimize quantized coefficient sequences, quantization factors, Huffman coding and Huffman coding region partition for MP3 encoding.
- It would be advantageous to provide for efficient optimization of quantization factors.
- In one aspect, the present application provides a method for optimizing audio encoding of a source sequence, the encoding being dependent on quantization factors, the quantization factors including a global quantization step size and scale factors. The method includes defining a cost function of the encoding of the source sequence, the cost function being dependent on the quantization factors. The method includes initializing fixed values of the scale factors; and determining values of the quantization factors which minimize the cost function by iteratively performing:
- determining, for the fixed values of the scale factors, a value of the global quantization step size which minimizes the cost function,
- fixing the determined value of the global quantization step size and determining values of scale factors which minimize the cost function, and fixing the determined values of the scale factors, and
- determining whether the cost function is below a predetermined threshold, and if so ending the iteratively performing.
- In another aspect, the present application provides a method for optimizing audio encoding of a source sequence based on minimizing of a cost function, the cost function being a function of quantization distortion and encoding bit rate, the cost function including λ as a function that represents the tradeoff of encoding bit rate for quantization distortion, the method comprising calculating λ as the function
wherein PE is Perceptual Entropy of an encoded frame, R is an encoding bit rate, M is the number of audio samples to be encoded, and c1, c2 and c3 are constants; and calculating the cost function using λ. - In another aspect, the present application provides an encoder for optimizing audio encoding of a source sequence, the audio encoding being dependent on quantization factors, the quantization factors including a global quantization step size and scale factors. The encoder includes a controller, a memory accessible by the controller, a cost function of an encoding of the source sequence stored in memory, the cost function being dependent on the quantization factors; and a predetermined threshold of the cost function stored in the memory. The controller is configured to access the cost function and predetermined threshold from memory, initialize fixed values of the scale factors, and determine values of the quantization factors which minimize the cost function by iteratively performing:
- determining, for the fixed values of the scale factors, a value of the global quantization step size which minimizes the cost function,
- fixing the determined value of the global quantization step size and determining values of scale factors which minimize the cost function, and fixing the determined values of the scale factors, and
- determining whether the cost function is below the predetermined threshold, and if so ending the iteratively performing.
- Reference is now made to
Figure 1 , which shows anMP3 encoding process 20 to which example embodiments may be applied. Generally, theMP3 encoding process 20 receivesdigital audio input 22 and produces a compressed or encodedoutput 32 in the form of a bitstream for storage and transmission. Theencoding process 20 may for example be implemented by an encoder such as a suitably configured computing device. InFigure 1 , continuous lines denote the time or spectral domain signal flow, and dash lines denote the control information flow. As shown, theencoding process 20 includesaudio input 22 for input to a time/frequency (T/F)mapping module 24 and apsychoacoustic model module 26. Also shown are a quantization andentropy coding module 28 and aframe packing module 30. Theencoding process 20 results in an encodedoutput 32 of theaudio input 22, for example for sending to a decoder for subsequent decoding. - The audio input 22 (in time domain) are first input into the T/
F mapping module 24, which converts theaudio input 22 into spectral coefficients. The T/F mapping module 24 is composed of three steps: pseudo-quadrature mirror filter (PQMF), windowing and modified discrete cosine transform (MDCT), and aliasing reduction. The PQMF filterbank splits a so-called granule (in MPEG I and II layer 3 each audio frame contains 2 and 1 granules respectively) of 576 input audio samples into 32 equally spaced subbands, where each subband has 18 time domain audio samples. The 18 time domain audio samples in each subband are then combined with their counterpart of the next frame, and processed by a sine-type window based on psychoacoustic modeling decisions. A long window, which covers a whole length of 36, addresses stationary audio parts. Long windowing with MDCT afterwards ensures a high frequency resolution, but also causes quantization errors spreading over the 1152 time-samples in the process of quantization. A short window is used to reduce the temporal noise to spread for the signals containing transients/attacks. In the short window, audio signals with a length of 36 are divided into 3 equal sub-blocks. In order to ensure a smooth transition from a long window to a short window and vice versa, two transition windows, long-short (start) and short-long (stop), which have the same size as a long window, are employed. - The
psychoacoustic model module 26 is generally used to generate control information for the T/F mapping module 24, and for the quantization andentropy coding module 28. Based on the control information from thepsychoacoustic model module 26, the spectral coefficients which are output from the T/F mapping module 24 are received by the quantization andentropy coding module 28, and are quantized and entropy coded. Finally these compressed bits streams are packed up along with format information, control information and other auxiliary data in MP3 frames, and output as the encodedoutput 32. - The MP3 syntax leaves the selection of quantization step sizes and Huffman codebooks to each encoder or encoding algorithm, which provides opportunity to apply rate-distortion consideration. A conventional MP3 encoding algorithm is now be described as follows, which employs a "hard decision quantization", a two nested loop search (TNLS) algorithm, and fixed or static Huffman codebooks.
- The MP3 quantization and
entropy coding module 28 first subdivides an entire frame of 576 spectral coefficients into 21 or 12 scale factor bands for a long window block (including long-short window and short-long window) or a short window block respectively. Each coefficient xri, i=0 to 575, is quantized by the following non-uniform quantizer:
where yi denotes the quantized index, nint denotes the nearest non-negative integer, global_gain is a global quantization step size which determines the overall quantization step size for the entire frame, and scale_factor[sb] is used to determine the actual quantization step size for scale factor band sb where the spectral coefficient xri lies (sb= 0 to 11 for short blocks, sb =0 to 20 for other blocks) to make the perceptually weighted quantization noise as small as possible. The formulaic determination of yi as in (2.1) may be referred to as "hard decision quantization". -
- Generally, each of the parameters listed in (2.2) may be referred to as a "scale factor", and all of which may be collectively referred to herein as "scale factors", as appropriate. global_gain and the scale factors may collectively be referred to herein as "quantization factors".
- In (2.2), sub_block is only used for short windows, and it refers to one of the 3 sub-blocks for a short window. scalefac[sub_block][sb] is a scale factor parameter for scale factor band sb to color the quantization noise. scalefac[sub_block][sb] are variable length transmitted according to scalefac_compress which occupies 4 bits (MPEG-1) or 9 bits (MPEG-2) in the side information of MP3 encoded frames. preflag is a shortcut for additional high frequency amplification of the quantized values. If preflag is set, the values of a fixed table pretab[sb] are added to the scale factors. preflag is never used in short windows (for the purposes of the standard). subblock_gain[sub_block] is the gain offset for the short window. scalefac-scale is a one-bit parameter used to control the quantization step size.
- The quantized spectral coefficients are then encoded by static Huffman coding, which utilizes 34 fixed Huffman codebooks. To achieve greater coding efficiency, MP3 subdivides the entire quantized spectrum into three regions. Each region is coded with a different set of Huffman codebooks that best match the statistics of that region. Specifically, at high frequencies, MP3 identifies a region of "all zeros". The size of this region can be deduced from the sizes of the other two regions, and the coefficients in this region don't need to be coded. The only restriction is that it must contain an even number of zeros since the other two regions group their values in 2- or 4-tuples. The second region, called "
count 1" region, contains a series of contiguous values consisting only of -1, 0, +1 just before the "zero" region, and is encoded in 4-tuples byHuffman codebook 32 or 33. Finally the low frequency region, called "big value" region, covers the remaining coefficients which are encoded in pairs. This region is further subdivided into 3 (for long window) or 2 (for short, long-short and short-long window) parts with each covered by a distinct Huffman codebook. - To minimize the quantization noise, a noise shaping method may be applied to find the proper global quantization step size global_gain and scale factors before the actual quantization. Some conventional algorithms use the TNLS algorithm to jointly control the bit rate and distortion. The TNLS algorithm consists of an inner (rate control) loop and an outer (noise control) loop. The task of the inner loop is to change the global quantization step size global_gain such that the given spectral data can just be encoded with the number of bits available. If the number of bits resulting from Huffman coding exceeds this number, the global_gain can be increased to result in a larger quantization step size, leading to smaller quantized values. This operation is repeated until the resulting bit demand for Huffman coding is small enough. The TNLS algorithm may require quantization step sizes so small to obtain the best perceptual quality. On the other hand, it has to increase to the quantization step sizes to enable coding at the required bit rate. These two requirements are conflicting. Therefore, this conventional algorithm does not guarantee to converge.
- In some example embodiments, soft decision quantization, instead of the hard decision quantization, is applied, and the corresponding purpose of quantization and entropy coding in MP3 encoding is to achieve the minimum perceptual distortion for a given encoding bit rate by solving, mathematically, the following minimization problem:
where xr is the original spectral signal, rxr is the reconstructed signal obtained from the quantized spectral coefficients y, P and H represent Huffman codebook region partition and Huffman codebooks selection respectively, q denotes the quantization factors including global_gain and scale factors, R(q) and R(y, P, H) are the bit rates to encode q and the quantized spectral coefficients y respectively, R 1 is the rate constraint, and D w (xr, rxr) denotes the weighted distortion measure between xr and rxr. Note that here y is not calculated according to (2.1) any more; instead, it is treated as a variable in a cost function involving the distortion and rates, and has to be determined jointly along with q, P, and H. Average noise-to mask ratio (ANMR) is used as the distortion measure. The noise-to mask ratio (NMR), the ratio of the quantization noise to the masking threshold, is a widely used objective measure for the evaluation of an audio signal. ANMR is expressed as
where N is the number of scale factor bands, w[sb] is the inverse of the masking threshold for scale factor band sb, and d[sb] is the quantization distortion, mean squared quantization error for scale factor band sb. -
- Reference is now made to
Figure 2 , which shows a flow diagram of anoptimization process 50 in accordance with an example embodiment. The exact order of steps may vary from those shown inFigure 2 in different applications and embodiments. It can also be appreciated that more or less steps may be required in some example embodiments, as appropriate. To find an optimum J λ, the parameters y, q, P and H are jointly optimized. The general framework for theprocess 50 has been outlined previously in Xu and E.-h. Yang, "Rate-distortion optimization for MP3 audio coding with complete decoder compatibility," in Proc. 2005 IEEE Workshop on Multimedia Signal Processing, Oct. 2005, the contents of which are herein incorporated by reference. Generally, theprocess 50 selects the quantized spectral coefficients y and Huffman codebook region division P, quantization factors q and Huffman codebook region selection H alternatively to minimize the Lagrangian cost J. The iterative searching for the parameters may be referred to as "soft-decision quantization" (rather than the formulaic "hard-decision quantization" of (2.1), described above). - Referring still to
Figure 2 , the iterative algorithm of theprocess 50 can be described as follows. Atstep 52, specify a tolerance ε as the convergence criterion for the Lagrangian cost J. Atstep 54, initialize a set of quantization factors q0 from the given frame of spectral domain coefficients xr with a Huffman codebooks selection mode H0; and set t=0. - At
step 56, qt and Ht are fixed or given for any t≥0. Find the optimal quantized spectral coefficients yt and Huffman codebook region division Pt by soft decision quantization, where yt and Pt achieve the minimum
where the inverse quantization function Q-1(q,y) is used to generate the reconstructed signal rxr. Denote J λ(yt , qt, Pt, Ht ) by -
-
- At
step 62, query whetheroptimization process 50 proceeds to step 66 and outputs the final y, q, P and H and ends atstep 68. If not, proceed to step 64 wherein t=t+1, and repeatsteps - Referring still to
Figure 2 , an example embodiment ofstep 56 will now be described in greater detail, with reference now toFigures 3 and 4. Figure 3 shows agraph 80 of an optimal path search algorithm for use in the process ofFigure 2 ; whileFigure 4 shows an optimal path of thegraph 80. - Without being limiting, consider for example the long window case. The
graph 80 is defined with 4 layers (shown as I, II, III, and IV) and 288 nodes in each layer as shown inFigure 3 . The 4 layers correspond to the three divisions of the big_value region and the count_1 region. Each state SL,i (L=I, ...,IV, 0 ≤ I <288) in layer L stands for two neighboring coefficients xr2i and xr 2i+1 to be quantized, since Huffman coding is always applied on 2-(for layer I, II, III) or 4-(for layers IV) tuples. Two special states, frame_begin and frame_end, denote the start and end of the frame respectively. Connection between any two states denotes a Huffman codebook region division decision pair: state SL,i may have incoming connections from states SM,j (M=1, ..., L; j=i-2 if L=IV, and j=i-1 otherwise), each of which represents the decision of assigning node i, i.e., coefficients xr2i and xr 2i+1 to the Huffman codebook region denoted by layer L. Note that not all the states and paths are compatible with the standard and the following syntax constraints should be observed for the construction of the graph 80: - a) States of
scale factor band 0 in layers II and III, states ofscale factor band 1 in layer III, and the second state in layer IV are illegitimate, and thus don't have any incoming and outgoing connections; - b) States after
scale factor band 15 in Layer I are not allowed; - c) A graph path cannot transverse more than 8 scale factor bands in layer II;
- d) The connections among layers I, II and III can only occur at the scale factor band boundaries, and the frame_begin state has only outgoing connections to states SI,0 and SIV,0 and frame_end; and
- e) The frame_end state has incoming connections from all legitimate states, with each connection from non-trailing state SL,i (0 ≤ i < 287) representing the decision of assigning the coefficients after node i to the zero region, that is, dropping that part of spectrum without Huffman encoding and transmission.
- Assign to each connection from previous states (no matter which layer they lie in) to state SL,i (0 ≤ i < 288) a cost which is defined as the minimum incremental Lagrangian cost of quantizing and Huffman encoding the coefficients of state SL,i (or states SLi-1 and SL,i if L=IV) by using the Huffman codebook selected for layer L. Specifically, this minimum incremental cost is equal to
where k=3 if L=IV, and k=1 otherwise, yj, j=2i-k, ... 2i, is the jth quantized coefficient, qj is the corresponding scale factor for yj, and rL (···) denotes the codeword length by using the Huffman codebook selected for layer L. Similarly, for the connection from state SL,i (0 ≤ i < 287) to the frame_end state, its cost is defined as - No cost is assigned to the connections from trailing state SL,288 to the frame_end state.
- With the above definitions, every sequence of connections from the frame_begin state to the frame_end state corresponds to a Huffman codebook region division of the entire frame with a Lagrangian cost. For example, the sequence of connection in
Figure 4 assignsscale factor band graph 80. Hence the optimal path from the frame_begin state to the frame_begin state, together with quantized coefficients along each connection that give the minimum cost defined by (3.7), achieves the minimum in step 56 (Figure 2 ) for any given q and H. - An elaborate step-by-step description of the path searching algorithm is described as follows, referring still to
Figures 3 and 4 . As an initialization, the algorithm preselects and stores the best quantized coefficients based on minimizing the Lagrangian cost of (3.7) for each legitimate state SL,i, and sets their associated cost as the cost of each connection to that state. The algorithm also recursively precalculates, for each state, the distortion/cost resulting from ending the frame at that state, i.e., the cost of its connection to the state frame_end. The algorithm begins with the state frame_begin by storing the cost of dropping the entire frame in Jframe_begin. Then, one proceeds to state SL,0 (L=I, .., IV), among which only states SI,0 and SIV,0 have incoming connections from the state frame_begin. The cost of each state is set to the cost of corresponding incoming connection, and added with the cost of dropping the remaining coefficients to get JI,0 and JIV,0, respectively. Proceeding to state SL,1 (L=I, .., IV), only states SL,1 has an incoming connection from states SI,0. Set its cost to the sum of the costs of state SI,0 and the connection between SI,0 and SI,1, and add it with the cost of dropping the remaining coefficients to get JI,1. Next, consider states SL,2 (L=I, .., IV), it may be observed that SIV,2 has two incoming connections from SIV,0 and SI,0 respectively. Here the connection from the state with less cost is chosen, and the costs of SIV,2 and JIV,2 are computed by adding it with corresponding incremental connection costs, respectively. Following the above cost computation rule, process all legitimate states: for each state SL,i, the best incoming connection is selected such that the accumulated cost (from frame_begin to SL,i ) can be minimized. Store this connection selection decision at that state, set the cost of SL,i to the accumulated cost, and then sum it with the cost of dropping the remaining coefficients to get JL,i . - Referring now to
Figure 4 , after traversing all the legitimate states, the path cost information, JL,i, L=I, .., IV, 0 ≤ i<288, is available. Obtain the minimum path cost Jmi = minL,i JL,i. By backtracking the path which gives Jmin with the help of the stored information in each state, the optimal quantized spectral coefficients y and region division P that solve the problem (3.4) may be obtained. - In a similar manner as described above, a three-layer graph could be constructed for other three window cases.
- Referring to
Figure 2 , step 58 will now be described in greater detail, with reference now toFigure 5. Figure 5 shows an example embodiment of aprocess 100 to be used instep 58 ofFigure 2 .Step 58 generally determines the quantization factors q (i.e., scale factors and global_gain) that minimize the combined cost of weighted distortion and bit rate for encoding or transmittal. Given the nonuniform quantizer and nonlinear bit rate for quantization factors in the standard, there is no direct formula to calculate the optimal quantization factors. Direct search through all combinations of global_gain, scalefac_compress, scalefac, scalfac_scale, and subblock_gain (for short windows) or preflag (for other windows) may be computationally complex. Take an MPEG-1 encoded long-block frame as an example. There are 256 different cases for global_gain, scalefac_compress, preflag and scalfac_scale have 16, 2 and 2 different cases respectively. There are 256 x 16 x 2 x 2 = 16384 different combinations to find the minimum combined cost. In some example embodiments, to reduce the computational complexity, themethod 100 includes the following alternating minimization procedure to minimize the combined cost. Generally, atstep 102 global_gain is determined while the scale factors are fixed, and atstep 104 the scale factors are determined while global_gain is fixed. This is repeated iteratively until the calculated rate-distortion cost is within a predetermined threshold. - At
step 102, update global_gain when scalefac, scalfac_scale and subblock _gain (for short windows) or preflag (for other windows) are fixed. In this case, the bit rate for the transmission of scale factors is fixed. Therefore, at this stage only the encoding distortion is minimized, while rate is not considered. The weighted distortion for scale factor band sb is
where s[sb]= global_gain-210-scale_factor[sb], I[sb] and l[sb+1]-1 are the start and end positions for scale factor band sb respectively, w[sb] is the inverse of the masking threshold for scale factor band sb. The total average weighted distortion Dw for an encoded frame could be expressed as -
- At
step 104, fix global_gain. Update the scale factors scalefac, scalfac_scale and subblock_gain (for short windows) or preflag (for other windows) to minimize the combined cost of weighted distortion and bit rate for transmitting the scale factors. As indicated from equation (3.9),
where global_gain has the value of 0 to 255, and scale_factor[sb] is equal to - preflag is equal to 0 or 1. The value of pretab[sb] is typically fixed and is of the form as shown in Table 1.
-
Table 1. The value of pretab[sb] for long windows. Sb 0 to 10 11 12 13 14 15 16 17 18 19 20 Preflag=0 0 0 0 0 0 0 0 0 0 0 0 Prefag=1 1 0 1 1 1 1 2 2 3 3 3 2 - scalefac_scale is equal to 0 or 1.
- The bit length of scalefac[sb] is determined by scalefac_compress, that is, scalefac_compress determines the number of bits used for the transmission of the scalefactors according to Table 2.
-
Table 2: The bit length for scalefac[sb] scalefac_compress slen 1 slen2 0 0 0 1 0 1 2 0 2 3 0 3 4 3 0 5 1 1 6 1 2 7 1 3 8 2 1 9 2 2 10 2 3 11 3 1 12 3 2 13 3 3 14 4 2 15 4 3 - As can be appreciated from Table 2, the bit length may be a first bit length for a first group of scale factor bands and the bit length may be a second bit length for a second group of scale factor bands. In Table 2 slen1 is the bit length of scalefac for each of
scalefactor bands 0 to 10, and slen2 is the bit length of scalefac for each of scalefactor bands 11 to 20. - From the above, it can be observed that a direct search for the minimum combined cost requires the computation of encoding costs for all combinations of scalefac_compress, scalfac_scale and preflag. This leads to 16 x 2 x 2 = 64 different combinations to find the minimum combined cost for each scalefactor band. Without intending to be limiting, the following example embodiment assumes that the encoding block is an MPEG-1 encoded, long-window frame. In some example embodiments, it is recognized that there are some redundant operations in the distortion computations. Therefore, some example embodiments provide for pre-generating a look-up table for those redundant operations, which are based on slen rather than searching through all combinations of scalefac_compress.
- From Table 2, the maximum length for slen1 is 4 while the maximum length for slen2 is 3 (as based on the MP3 standard). When slen1 and s len2 are given, in some example embodiments, one can find the minimum encoding distortion for each scalefactor band and the corresponding scalefac[sb] which generates the minimum encoding distortion. Hence, when preflag and scalfac_scale are fixed, there only needs to be calculated 5 (the first 11 bands) or 4 (the last 10 bands) different cases of encoding distortion for each scale factor band, rather than calculate the encoding distortion 16 times for different scalefac_compress. In each case, the pre-calculated encoding distortion is minimized with a certain value for scalefac[sb] given the length slen1 or slen2.
- Let's denote dist[sb][slen] as the minimum weighted distortion for scale factor band sb, where sb=0, ..., 20 and slen=0, ..., 4. Denote sf[sb][slen] as the value for scalefac[sb] such that the weighted distortion is minimized for scale factor band sb when the bit length used for transmitting scalefac[sb] is slen. To generate a look-up table for each scale factor band, apply the following approach given the fixed values for global_gain, scalfac_scale and preflag. Without loss of generality, the following example embodiment considers the first 11 scale factor bands for an MPEG-1 encoded, long-window frame.
- Assume s[sb] in equation (3.9) can be freely chosen. That is, s[sb] is not restricted by the value of scalefac[sb] to be one of the 16 integer numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15). Apply the minimum mean square error criterion to find the minimum weighted distortion for (3.9). That is, let
- Denote sg[sb]=s[sb]+210, The corresponding value for scalefac[sb] is (global_gain - sg[sb])/2(1+sCaifac_scale) - preflag · pretab[sb]. Denote this value as T. scalefac[sb] cannot be freely chosen in reality (as defined by the standard), that is, it must be constrained to one of the 16 integer numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15). In some example embodiments, the value of scalefac[sb] can be determined using the following algorithm. Generally, it is determined whether T exceeds encoding within slen, and if so constraining T to within slen:
If slen=0
Else (slen≠0)
if T≤0
for slen = 1 to 4
let sf[sb][slen] = 0, and let dist[sb][slen] = dist[sb][0].
else if T ≥ 15
for slen=1 to 4
let sf[sb][slen]=2slen-1, and calculate dist[sb][slen] using
equation (3.9).
else
let sf[sb][4]=T (If T is not an integer, choose one of the two nearest integers to T which has smaller weighted distortion), calculate
dist[sb][4] using equation (3.9)
for slen=3 down to 1
if sf[sb][slen+1] ≥ 2slen-1
let sf[sb][slen]=2slen-1.
else
let sf[sb][slen]=sf[sb][slen+1].
calculate dist[sb][slen] using equation (3.9). - Totally there are 20 different cases (5 slen1 x 2 preflag x 2 scalfac_scale) of encoding distortion for each of the first 11 scale factor bands and 16 different cases (4 s/en2 x 2 preflag x 2 scalfac_scale) of encoding distortion for each of the last 10 scale factor bands. As the setting of preflag only affects the last 10 scale factor bands, the number of different cases of encoding distortion to be computed for each of the first 11 scale factor bands is reduced to 10 (5 slen1 x 2 scalfac_scale). In other words, the cost function is minimized with respect to preflag for only one set of scale factor bands, being the higher frequency scale factor bands 11 to 20. In addition, there exists one redundant case for each scale factor band if scalefac[sb] is equal to 0 (i.e., (3.16) may be calculated once). As a result, in some example embodiments, there are 9 (the first 11 scale factor bands) or 15 (the last 10 scale factor bands) different cases of encoding distortion for each scale factor band.
- After generating the above table based on encoding distortion, what remains is the calculation of the total Lagrangian cost by calculating (3.3). As described above with respect to (3.3), the total Lagrangian cost is the addition of the encoding distortion and the bit rate. Therefore, what remains is the addition of bit rate to calculate the combined cost. For example, the distortion based on bit rate for the transmission of all scale factors can also be looked up from a pre-generated table, as is known in the art. Similarly, for other window cases, a similar approach could be applied to reduce the computational complexity.
- At
step 106, repeat steps 102 and 104 until the decrease of the combined cost is below a prescribed threshold. If the predetermined threshold is reached, atstep 110 output the final global_gain and scale factors (scalefac, scalfac_scale, preflaglsubblock_gain), and then ends at step 112 (or proceed to the next step in method 50 (Figure 2 )). - As the
iterative method 100 generally converges after two rounds of iteration, the number of different cases to be computed for each scale factor band of an MPEG-1 encoded, long-window frame has been reduced from 16384 to 18 (the first 11 bands) or 30 (the last 10 bands). - The particular quantization factors or scale factors to be determined may depend on the particular application or coding scheme, and may not be limited to the parameters global_gain, scalefac, scalfac_scale, and preflag/subblock_gain.
- Referring now to
Figure 2 , step 60 will now be described. Given Huffman coding region division P, the quantization factors q and quantized spectral coefficients y, determining the Huffman codebook H may be performed as follows: for each region, every Huffman codebook that has encodable value limit larger than or equal to the greatest coefficient amplitude of that region is considered, and the one with the minimum codeword length is selected. - Implementation and simulation results will now be described. In regards to (3.3), the estimation of lambda (λ) will now be described in greater detail. In conventional systems, bisection methods may be used to determine for a final λ. This may require a high computational complexity which is proportional to the number of iterations over the optimization algorithm described in the last section. As recognized herein, in some example embodiments, by analyzing the relationship between Perceptual Entropy, signal to noise ratio, signal to mask ratio, encoding bit rate and the number of audio samples to be encoded, the final λ was estimated using the following formula in a trellis search algorithm for the optimization of advance audio coding (AAC),
where PE is Perceptual Entropy of an encoded frame, R is the encoding bit rate, and M is the number of audio samples to be encoded. c 1, c2 and c 3 are determined from the experimental data using the least square criterion. This is for example generally described in C. Bauer and M. Vinton, "Joint optimization of scale factors and Huffman codebooks for MEPG-4 AAC," in Proc. of the 2004 IEEE workshop on Multimedia Signal Processing, pp. 111-114, 2004; and C. Bauer and M. Vinton, "Joint optimization of scale factors and Huffman codebooks for MEPG-4 AAC," in IEEE Trans. on Signal Processing, vol. 54, pp. 177-189, Jan. 2006, both of which are incorporated herein by reference. - In the experiment, 16 RIFF WAVE files with a sampling rate of 44.1 khz from a sound test file were used. The initial value for λ was arbitrarily selected, and the bisection method was used to find the final value for λ. The optimized MP3 encoded files were generated for each of the 16 RIFF WAVE test files at the encoding bit rates of 32, 40, 48, 56, 64, 80, 96, 112, 128, 144, 160, 192, 224, 256 and 320 kbps. For each tested file, tested values of Perceptual Entropy and λ at different encoding bit rates were recorded. As the values of Perceptual Entropy are usually in the range of 100 to 3000, tested data outside this range was discarded. Next, uniformly quantize the values of tested Perceptual Entropy with a quantization step size of 100, and calculated the mean value and standard deviation for the tested λ for each possible encoding bit rate and perceptual entropy pair.
- To determine the values of c1, c2 and c 3, a non-linear regression progress within MATLAB optimization toolbox was used in some example simulations. Specifically, use the following MATLAB function
-
- The average number of iterations was tested over the Lagrangian multiplier if the formula (4.1) with the above estimated coefficient is used as the initial point for the bisection search. The average number of iterations over the Lagrangian multiplier is 1.5. On the other hand, the average number of iterations over the Lagrangian multiplier ranges from 4 to 8 if an arbitrary number is used as the initial point. Therefore, on the average, using (4.1) as the initial point can run 4 times as fast as the method in which an arbitrary initial point is used.
- Implementation and simulation results of the
optimization process 50 will now be described, referring now toFigures 6 to 9 . Generally, the performance of example embodiments is implemented based on two MP3 encoders: ISO reference codec and LAME 3.96.1. For each case, the iterative optimization algorithm uses the original encoder output as the initial points.Figure 6 shows agraph 140 of performance characteristics of an example embodiment, showing a comparison of the method 50 (Figure 20) for encoding of audio file waltz.wav as compared to ISO reference codec.Figure 7 shows agraph 150 of performance characteristics of an example embodiment, for encoding of audio file waltz.wav as compared to LAME.Figure 8 shows agraph 160 of performance characteristics of an example embodiment, for encoding of audio file vioin.wav as compared to ISO reference codec.Figure 9 shows agraph 170 of performance characteristics of an example embodiment, for encoding of audio file violin.wav as compared to LAME. - The LAME MP3 encoder features a psychoacoustic model, joint stereo encoding and variable bit-rate encoding. However, LAME still uses the basic structure of typical TNLS. In LAME 3.96.1, a refining TNLS is used to minimize the total noise to masking ratio for an entire frame after the successful termination of search process given its typical TNLS. Specifically, during each outer loop, the band with maximum noise to masking ratio is amplified and the best result based on total noise to mask ratio is stored.
- The method 50 (
Figure 2 ) is implemented as described above. For each case, the perceptual model, joint stereo encoding mode and window switching decision are kept intact.Figure 6 shows the rate-distortion performance of the method 50 (Figure 2 ) (denoted as "RD optimization" in the graph 140) applied to ISO reference encoder, when compared to a conventional or normal ISO reference encoder implementing TNLS, in constant bit-rate mode for waltz.wav. The test file may for example be encoded at 48khz, 2 channel, 16 bits/sample, 30 seconds. InFigure 6 , "ISO-HO" represents the optimal Huffman tables used for Huffman coding, while "ISO-NH" means that the first Huffman table satisfying the coding limit is selected for each Huffman coding region. The vertical axes denote the average noise to mask ratio over all audio frames. FromFigure 6 , the method 50 (Figure 2 ) can achieve significant performance gain over the ISO reference encoder. For instance, at 320kbps the proposed optimization algorithm achieves 4.57dB and 2.75dB ANMR gains over ISO-NH and ISO-HO respectively. The ANMR of the optimized algorithm at 32kbps is similar to that of ISO reference encoder at 40kbps, which corresponds to equivalent 20% compression rate reduction. -
Figure 7 depicts the rate-distortion performance of the method 50 (Figure 2 ) (also denoted as "RD optimization) applied to LAME when compared to the LAME reference encoder (implementing conventional TNLS) in constant bit-rate mode for waltz.wav. It is shown separately from ISO reference encoder because ISO reference encoder and LAME adopt different perceptual models. For an unbiased comparison, in some example embodiments the LAME encoder disables the functions of amplitude scaling and low pass filter. InFigure 7 , "LAME" means that the audio file is compressed using LAME's normal compression mode. As shown, the method 50 (Figure 2 ) outperforms LAME in terms of compression performance. At 96kbps, the proposed optimization algorithm achieves about 1.34dB ANMR gain over LAME. -
Figures 8 and 9 compare the compression performance of the method 50 (Figure 2 ) for the music file violin.wav (MPEG lossless audio coding test file, 48khz, 2 channel, 16 bits/sample, 30 seconds) in constant bit-rate mode.Figure 8 shows results from ISO reference encoder, whileFigure 9 shows results from LAME. It may be observed that "RD optimization" has improved rate-distortion over the conventional reference encoders. Similar results may be observed for other test music files. - Referring now to
Figure 2 , the computational complexity of themethod 50 will now be described. Given the value of λ, the number of iterations in the iterative joint optimization algorithm has a direct impact on the computational complexity. Experiments show that by setting the convergence tolerance ε to 0.005, the iteration process is observed to converge after 2 loops in most cases, that is, most of the gain achievable from full joint optimization is obtained within two iterations. This is the same to the iterative quantization factor q updating instep 58. InStep 56, the search range for yj is set to [yhj-a, yhj+a], where yhj is the jth quantized coefficient from hard decision quantization (e.g. yj is determined from (2.1)) and a is a fixed integer. Experiments show that further expansion of the search range for yj beyond a = 2 does not significantly improve compression performance. In constant bit-rate mode, the average number of iterations over the Lagrangian multiplier is 1.5 if the formula (4.1) is used as the initial point. O n the other hand, the average number of iterations over the Lagrangian multiplier ranges from 4 to 8 if an arbitrary number is used as the initial point. - Table 3 lists the computation time (in seconds) on a Pentium PC, 2.16GHZ, 1G by tes of RAM to encode violin.wav and waltz.wav at different transmission rates for the
method 50 based on LAME reference codec. -
Table 3. Computation time in seconds for different MP3 encoders Bit rates (kbps) 96 112 128 160 192 Waltz.wav 27 23 21 21 16 Violin.wav 23 22 20 16 15 - From Table 3 the proposed optimization algorithm generally reaches real time throughput, which suggests that the
method 50 is computationally efficient. As shown in Table 3, the computation time is generally less than 30 seconds. The computation time for ISO-based encoders is not listed, but are generally less-efficient than LAME-based encoders in both the computation time and compression performance. - Reference is now made to
Figure 10 , which shows anencoder 300 in accordance with an example embodiment. Theencoder 300 may for example be implemented on a suitable configured computer device. Theencoder 300 includes a controller such as amicroprocessor 304 that controls the overall operation of theencoder 300. Themicroprocessor 304 may also interact with other subsystems (not shown) such as a communications subsystem, display, and one or more auxiliary input/output (I/O) subsystems or devices. Theencoder 300 includes amemory 304 accessible by themicroprocessor 304.Operating system software 306 andvarious software applications 308 used by the microprocessor 302 are, in some example embodiments, stored inmemory 304 or similar storage element. For example,MP3 software application 310, such as the ISO-based encoder or LAME-based encoder described above, may be installed as one of thevarious software applications 308. The microprocessor 302, in addition to its operating system functions, in example embodiments enables execution ofsoftware applications 308 on the device. - The
encoder 300 may be used for optimizing performance of MP3 encoding of a source sequence. Specifically, theencoder 300 may enable themicroprocessor 304 to determine quantization factors (for example including a global quantization step size and scale factors) for the source sequence. Thememory 304 may contain a cost function of an encoding of the source sequence, wherein the cost function is dependent on the quantization factors. Thememory 304 may also contain a predetermined tolerance of the cost function stored in thememory 304. Instructions residing inmemory 304 enable the microprocessor 203 to access the cost function and predetermined tolerance frommemory 304, determine the quantization factors which minimize the cost function within the predetermined tolerance, and store the determined quantization factors inmemory 304 for MP3 encoding of the source sequence. Generally, an iterative method is performed such that global_gain is determined while the scale factors are fixed, and the scale factors are determined while g/obal_gain is fixed. This is repeated until a calculated rate-distortion cost is within a predetermined threshold. For example, theMP3 software application 310 may be used to perform MP3 encoding using the determined quantization factors. - In another example embodiment, the
encoder 300 may be configured for optimizing of parameters including quantization factors, in a manner similar to the example methods described above. For example, theencoder 300 may be configured to perform the method 50 (Figure 2 ). - While the foregoing has been described with respect to MP3 encoding, it may be appreciated by those skilled in the art that example embodiments may be adapted to or implemented by other forms of signal encoding or audio signal encoding, for example Advanced Audio Coding.
- While example embodiments have been described in detail in the foregoing specification, it will be understood by those skilled in the art that variations may be made without departing from the scope of the present application.
Claims (15)
- A method for optimizing audio encoding of a source sequence, the encoding being dependent on quantization factors, the quantization factors including a global quantization step size and scale factors, the method comprising:defining a cost function of the encoding of the source sequence, the cost function being dependent on the quantization factors;initializing fixed values of the scale factors; anddetermining values of the quantization factors which minimize the cost function by iteratively performing:determining, for the fixed values of the scale factors, a value of the global quantization step size which minimizes the cost function,fixing the determined value of the global quantization step size and determining values of scale factors which minimize the cost function, and fixing the determined values of the scale factors, anddetermining whether the cost function is below a predetermined threshold, and if so ending the iteratively performing.
- The method claimed in claim 1, wherein the cost function is based on a distortion of the encoding of the source sequence and further based on a tradeoff function that represents a tradeoff of a rate for distortion, said rate being a transmission bit rate of the encoding of the source sequence.
- The method claimed in claim 2, wherein, in the step of fixing the determined value of the global quantization step size and determining values of scale factors which minimize the cost function, the distortion is obtained from a pre-generated table.
- The method claimed in claim 2, wherein the tradeoff function includes λ, the method further comprising:calculating λ as:
wherein PE is Perceptual Entropy of an encoded frame, R is the rate, M is a number of audio samples to be encoded, and c1, c2 and c3 are constants; andcalculating the cost function using λ. - The method claimed in claim 1, wherein the determining of the value of global quantization step size includes calculating:
wherein
wherein xri is the source sequence, scale_factor[sb] is a quantization step size for scale factor band sb, l[sb] and l[sb+1]-1 are start and end positions for scale factor band sb respectively, w[sb] is an inverse of the masking threshold for scale factor band sb, and yi is a quantized spectral coefficient of the source sequence. - The method claimed in claim 1, further comprising constraining the scale factors to within a bit length.
- The method claimed in claim 10, wherein the bit length is a first bit length for a first group of scale factor bands and the bit length is a second bit length for a second group of scale factor bands.
- The method claimed in claim 1, wherein the scale factors include a parameter scalefac being a scale factor for a particular scale factor band, the method further comprising constraining scalefac to within a bit length.
- The method claimed in claim 8, wherein the bit length is a first bit length for a first group of scale factor bands and the bit length is a second bit length for a second group of scale factor bands.
- The method claimed in claim 1, wherein the scale factors include a parameter scalefac being a scale factor for a particular scale factor band, the method further comprising:calculating a value of scalefac which minimizes the cost function; anddetermining whether the calculated value of scalefac exceeds encoding within a bit length, and if so constraining scalefac to within the bit length.
- The method claimed in claim 14, further comprising:calculating the cost function for scalefac = 0 for a scale factor band; andstoring in a memory the calculated cost function for scalefac = 0 for subsequent retrieval.
- The method claimed in claim 1, wherein the audio encoding is MPEG I/II Layer-3 encoding.
- The method claimed in claim 1, wherein the encoding is further dependent on quantized spectral coefficients, Huffman codebooks, and Huffman coding region partition, the method further including minimizing the cost function with respect to the quantized spectral coefficients, the Huffman codebooks, and the Huffman coding region partition.
- An encoder for optimizing audio encoding of a source sequence, the audio encoding being dependent on quantization factors, the quantization factors including a global quantization step size and scale factors, the encoder comprising:a controller;a memory accessible by the controller, a cost function of the encoding of the source sequence stored in memory, the cost function being dependent on the quantization factors; anda predetermined threshold of the cost function stored in the memory,
wherein the controller is configured to:access the cost function and predetermined threshold from memory,initialize fixed values of the scale factors, anddetermine values of the quantization factors which minimize the cost function by iteratively performing:determining, for the fixed values of the scale factors, a value of the global quantization step size which minimizes the cost function,fixing the determined value of the global quantization step size and determining values of scale factors which minimize the cost function, and fixing the determined values of the scale factors, anddetermining whether the cost function is below the predetermined threshold, and if so ending the iteratively performing.
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