WO1998015947A2 - Parallel spectral reed-solomon encoder and decoder - Google Patents
Parallel spectral reed-solomon encoder and decoder Download PDFInfo
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- WO1998015947A2 WO1998015947A2 PCT/US1997/018108 US9718108W WO9815947A2 WO 1998015947 A2 WO1998015947 A2 WO 1998015947A2 US 9718108 W US9718108 W US 9718108W WO 9815947 A2 WO9815947 A2 WO 9815947A2
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- spectral domain
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
- H03M13/13—Linear codes
- H03M13/15—Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes
- H03M13/151—Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes using error location or error correction polynomials
Definitions
- Optical communication systems typically operate at very high speeds and may involve a limited degree of parallelism via wavelength and/or pol.arization multiplexing. Space or time division multiplexing may significantly increase the parallelism of optical communication channels for use within computer interconnect environments. To ensure efficient utilization of channel bandwidth and avoid unwanted data bottlenecks, it is necessary to implement high speed error decoders within such systems.
- Optical memories offer high storage capacities, and with volume storage techniques, can achieve very high aggregate data rates via parallel access.
- Optical memories however, like other storage media are prone to errors owing to media defects, noise and faulty read/write systems.
- Conventional error correction techniques involve decoding in a time-sequential (i.e., serial) fashion; however, the highly parallel nature of the data retrieved from page access optical memory, for example, requires an alternate solution, since such a serial decoding scheme can produce a severe bottleneck in the system.
- information data which comprises an encoder configured to convert the user
- the encoder further supplies the encoded data to a medium for either transmission or
- a decoder is also provided which is coupled to the medium for decoding the encoded
- Fig. 1 illustrates a data encoding/decoding system in accordance with the present
- Fig. 2 illustrates a block diagram of a parallel Berlekamp Algorithm circuit in accordance
- Fig. 3 is a block diagram of a parallel Fourier transform circuit
- Fig. 4 is a detailed block diagram of the parallel Berlekamp Algorithm circuit
- Fig. 5 is a detailed block diagram of a parallel Recursive Extension circuit in accordance
- Figs. 6(a) and 6(b) are block diagrams illustrating a serial decoder and a parallel decoder
- Fig. 7 illustrates plots of very large scale integrated circuit area as a function of code-rate
- Fig. 8 illustrates plots of power dissipation as a function of block size (n) for serial
- Fig. 9 illustrates plots of information rate as a function of block size for serial decoders
- Fig. 10 illustrates plots of VLSI area for parallel space domain decoders and a decoders in
- Fig. 1 illustrates a functional block diagram of an
- system 100 includes an encoder 110 which encodes received user information data in accordance
- a medium or channel 120 e.g., an optical medium
- the encoded data can be supplied to an electrical-to-optical conversion element (not shown)
- decoder 130 Upon receipt of the encoded binary data, decoder 130
- optical to electrical conversion elements decodes the encoded binary data
- user information data is typically segmented into symbols
- each symbol being m bits in length, where m is an integer.
- k symbols k being
- information data is treated as spectral domain data and a plurality of error correcting symbols
- the resulting group of symbols is referred to as a codeword vector C of
- n being an integer greater than k, such that there are n-k zero symbols appended to the k
- Circuit 112 next acts on the symbols of codeword C in parallel to
- Vector r which is the signal received from channel 120, is next detected at receiver 130.
- Circuit 131 constitutes spectral domain
- conversion means which in this example, typically performs an F 4 T on the received vector r to
- error vector E are thus obtained directly from the F 4 T of the received vector r, and supplied to
- BA Berlekamp Algorithm
- locator polynomial are used to calculate each component of the error vector E. Once E is known,
- the error locator polynomial is defined as:
- ⁇ in the above equation is the nth root of unity over a
- the error locator polynomial is defined such that if the ith symbol of
- the error vector can have at most t symbol
- Stage 1 until Stage t and from then on remains the same until the last stage.
- FIG. 2 illustrates the parallel pipeline architecture of BA circuit 132 in accordance with
- Stage 1 to Stage t the associated integrated circuit area also increases.
- the t* stage the t* stage
- the integrated circuit area occupied by Stage 2t is nearly half the area of
- the parallel structure shown in Fig. 2 advantageously achieves a data pipeline
- Stage 1 this stage performs its task and the results are loaded into the
- circuits may be limited by gate delays, long metal wire capacitances do not significantly
- RE Recursive Extension
- error vector E is added to vector R to obtain codeword
- Error vector E can be obtained from the error locator polynomial using RE. In the space
- Equation 4 above takes into account that the maximum degree of the error locator polynomial is
- [5] ⁇ £,-_ ⁇ + ⁇ j£,-_3 + .. . + A,£ _ t .
- the architecture of the RE functional module also has a data pipeline
- RE typically have a similar construction, thus greatly simplifying the design process.
- RAM delay random access memory
- RE circuit 133 supplies error vector E to a comparison means, which in this example comprises a
- codeword vector C The zero symbols attached to vector C are then truncated, thereby leaving
- Decoder 134 including circuits 131, 132 and 133 will next be described in greater detail
- Fourier transform circuit 131 will first be described. Fourier transform circuit 131 is
- Cooley-Tukey algorithm itself is described in M. A. Neifeld et al., "Parallel Error
- Finite field Fourier transforms (F 3 Ts) are operable over a particular mathematical set
- DFTs Preferably, the DFT is modified for operation over the finite field and becomes:
- ⁇ is the nth root of unity over the finite field, v ; is the i th element of the space domain
- Cooley-Tukey F 4 T algorithm is applicable for cases when n is a composite number
- Cooley-Tukey F 4 T formula each receive n numbers so that the inner sum is
- n" is a composite number, then they in turn can be simplified by another application of the F 3 T.
- a first group of five symbols is supplied in parallel to block 310-1, and second and third groups of five symbols each are similarly fed to blocks 310-2 and
- blocks 310-2 and 310-3 have a similar construction as
- Each column includes five finite field multiplication stages
- each multiplier receives a corresponding input symbol. Further, each multiplier multiplies
- m bit XOR gate 313-1 outputs one of the 15 intermediate symbols.
- blocks 310-2 to 310-3 respectively output groups of five intermediate symbols
- the upper blocks constitute a 3 point F 3 T, and since each of blocks 310-1 to 310-3
- Each of lower blocks 320-1 to 320-3 receives the 15 intermediate symbols in parallel, and
- the lower blocks thus constitute a five point
- Lower blocks 320-1 to 320-3 have a similar construction and
- the multiplier in the lower blocks are arranged in rows, e.g. row 321 of lower block 320-1.
- the outputs are arranged in rows, e.g. row 321 of lower block 320-1.
- the upper and lower blocks constitute an F T and operate to multiply an unknown finite
- FIG. 4 shows a detailed block diagram of an arbitrary stage of
- Latches 410, 420 and 430 output the syndrome symbols, ⁇ °(x) and B°(x) to finite field multiplication stage 435, which includes
- Symbol ⁇ [ is next supplied to Symbol Inverse block 437, which outputs symbol ⁇ , '1 , the
- Block 440 includes an array 441 of finite field multiplication stages M, which operate
- the desired error locator polynomial ⁇ (x) is obtained.
- decoding process involves computing the error vector using recursive extension (RE).
- RE circuit recursive extension
- Each of Stages 1 through k of RE circuit 133 outputs a respective symbol of error vector
- Stage 1 (block 510) outputs E 0
- stages 2, 3, . . . k output symbols E réelle E 2
- stages 2, 3, . . . k output symbols E réelle E 2
- Block 510 illustrates Stage 1 in greater detail. It is understood that Stages 2-k have a similar construction as Stage 1.
- Block 510 outputs symbol E 0 based on the last t syndrome symbols of vector R
- decoder 130 An example of the operation of decoder 130 will be presented below.
- ⁇ is the 15 th root of unit over a mathematical set known as a finite field, which is obtained
- the vector c is then transmitted over channel 120, as discussed above. Assuming the
- ⁇ (x) ⁇ 1 x 2 + ⁇ ⁇ x + l;
- the outputs of the fourth stage of BA circuit 132 are:
- ⁇ (x) ⁇ 3 x 2 + ⁇ 13 x + 1;
- the outputs of the fifth stage of BA circuit 132 are:
- ⁇ (x) ⁇ 4 x 3 + ⁇ 13 x 2 + ⁇ 13 x + 1 ;
- ⁇ (x) ⁇ ⁇ x 3 + ⁇ 3 x 2 + ⁇ 9 x + 1;
- the desired error locator polynomial is therefore:
- ⁇ (x) ⁇ 1 'x 3 + ⁇ 3 x 2 + ⁇ 9 x + 1.
- RE circuit 133 the following parameters are input to RE circuit 133:
- E 0 A, E I4 + ⁇ 2 + E, 3 + ⁇ 3 E 12 .
- the decoder was fabricated in a 6mm x 4mm MOSIS
- one symbol of the received vector is provided as input to the
- Each decoder e.g., blocks 610-1, 620-1 and 630-1, will then
- aggregate decoding data rate achieved is P times that of a single serial decoder.
- time domain decoding is unfolded to
- Fig. 7 illustrates very large scale integrated circuit (VLSI) area as a function of code rate
- VLSI area than an array of serial decoders for codes of all block sizes considered.
- parallel decoders in accordance with the present invention offer a much better implementation efficiency than the array of serial decoders, as represented by more than an order
- V is 5 V
- a typical value of V is 5 V
- the total power dissipated by the parallel decoder is less than 1W.
- Information rate is an additional performance metric to be considered.
- the total chip area is assumed to be fixed at 1 cm 2
- the clock rate is assumed to be
- the total transistor count of the spectral decoder was 33,000.
- the chip was fabricated using a 2 ⁇ m CMOS process and SPICE simulation for this process
- the Euclidean algorithm is used to determine the error locator polynomial, followed by a
- search functional modules have parallel pipeline processing and each of the funcitonal modules
- the parallel spectral decoder has improved power dissipation, and has higher page rates and
- the present invention can be used in applications involving a high degree of parallelism
- an input shift register can be used to facilitate high
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- Physics & Mathematics (AREA)
- Probability & Statistics with Applications (AREA)
- Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Physics (AREA)
- Algebra (AREA)
- General Physics & Mathematics (AREA)
- Pure & Applied Mathematics (AREA)
- Error Detection And Correction (AREA)
- Detection And Correction Of Errors (AREA)
- Detection And Prevention Of Errors In Transmission (AREA)
Abstract
Description
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Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
AU58944/98A AU5894498A (en) | 1996-10-08 | 1997-10-07 | Parallel spectral reed-solomon encoder and decoder |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US2795296P | 1996-10-08 | 1996-10-08 | |
US60/027,952 | 1996-10-08 |
Publications (3)
Publication Number | Publication Date |
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WO1998015947A2 true WO1998015947A2 (en) | 1998-04-16 |
WO1998015947A9 WO1998015947A9 (en) | 1998-07-02 |
WO1998015947A3 WO1998015947A3 (en) | 1998-08-20 |
Family
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Application Number | Title | Priority Date | Filing Date |
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PCT/US1997/018108 WO1998015947A2 (en) | 1996-10-08 | 1997-10-07 | Parallel spectral reed-solomon encoder and decoder |
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AU (1) | AU5894498A (en) |
WO (1) | WO1998015947A2 (en) |
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN111476137A (en) * | 2020-04-01 | 2020-07-31 | 北京埃德尔黛威新技术有限公司 | Novel pipeline leakage early warning online correlation positioning data compression method and equipment |
Citations (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US4336612A (en) * | 1978-01-17 | 1982-06-22 | Mitsubishi Denki Kabushiki Kaisha | Error correction encoding and decoding system |
US4675869A (en) * | 1984-02-29 | 1987-06-23 | U.S. Philips Corporation | Fast decoder and encoder for Reed-Solomon codes and recording/playback apparatus having such an encoder/decoder |
US4763332A (en) * | 1987-03-02 | 1988-08-09 | Data Systems Technology Corp. | Shared circuitry for the encoding and syndrome generation functions of a Reed-Solomon code |
US5384786A (en) * | 1991-04-02 | 1995-01-24 | Cirrus Logic, Inc. | Fast and efficient circuit for identifying errors introduced in Reed-Solomon codewords |
-
1997
- 1997-10-07 AU AU58944/98A patent/AU5894498A/en not_active Abandoned
- 1997-10-07 WO PCT/US1997/018108 patent/WO1998015947A2/en active Application Filing
Patent Citations (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US4336612A (en) * | 1978-01-17 | 1982-06-22 | Mitsubishi Denki Kabushiki Kaisha | Error correction encoding and decoding system |
US4675869A (en) * | 1984-02-29 | 1987-06-23 | U.S. Philips Corporation | Fast decoder and encoder for Reed-Solomon codes and recording/playback apparatus having such an encoder/decoder |
US4763332A (en) * | 1987-03-02 | 1988-08-09 | Data Systems Technology Corp. | Shared circuitry for the encoding and syndrome generation functions of a Reed-Solomon code |
US5384786A (en) * | 1991-04-02 | 1995-01-24 | Cirrus Logic, Inc. | Fast and efficient circuit for identifying errors introduced in Reed-Solomon codewords |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN111476137A (en) * | 2020-04-01 | 2020-07-31 | 北京埃德尔黛威新技术有限公司 | Novel pipeline leakage early warning online correlation positioning data compression method and equipment |
CN111476137B (en) * | 2020-04-01 | 2023-08-01 | 北京埃德尔黛威新技术有限公司 | Novel pipeline leakage early warning online relevant positioning data compression method and device |
Also Published As
Publication number | Publication date |
---|---|
AU5894498A (en) | 1998-05-05 |
WO1998015947A3 (en) | 1998-08-20 |
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