CN114938259A - Probability shaping PAM-8 signal short-distance transmission method and system - Google Patents
Probability shaping PAM-8 signal short-distance transmission method and system Download PDFInfo
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Abstract
The invention relates to a short-distance transmission method of a probability shaping PAM-8 signal, a PAS coder deployed at a sending end receives a transmitting signal and carries out coding processing on the transmitting signal to generate a symbol sequence after probability shaping, and the PAS coder carries out joint coding by an ELA coder and an LDPC coder; and recovering the received signal received by the receiving end by utilizing an equalizer to obtain a recovered signal, decoding the recovered signal by a PAS decoder to obtain a transmitting signal, wherein the equalizer comprises a feedforward equalizer, a 2-order Waltara equalizer and a 2-order simplified Waltara equalizer, and the 2-order simplified Waltara equalizer only keeps an inner core of the 2-order Waltara equalizer. The invention adopts the combined coding mode of the ELA coder and the LDPC coder to obtain the PS-PAM-8 signal with better signal, obviously improves the feasibility of the scheme and enables the scheme to be suitable for short-distance IM/DD PAM-8 signal transmission.
Description
Technical Field
The invention relates to the technical field of optical communication networks, in particular to a method and a system for short-distance transmission of probability shaping PAM-8 signals.
Background
To handle the large capacity connections in a data center, Intra-data-center (IDC) networks require high-speed optical interconnection technology with low power consumption and low complexity. The Intensity-modulation Direct-detection (IM/DD) technique has advantages over the coherent technique because it has simpler and lower cost components, such as lasers, modulators, and receivers. Among various Modulation formats, Pulse-amplitude Modulation (PAM) signals are simpler to implement, and thus, high-speed PAM-4 signals are widely studied.
Compared to the PAM-4 Signal, the PAM-8 Signal can carry more information, but at the cost of more complex Digital Signal Processing (DSP). In addition, the robustness of the PAM-8 signal can be enhanced by using Probability Shaping (PS) and a non-linear equalizer. Thus, by indexing the lowest energy symbol and increasing its probability of occurrence, the PS-PAM-8 signal outperforms the uniform PAM-8 signal. Furthermore, the combination of PS and Forward Error Correction (FEC) can implement Probabilistic Amplitude Shaping (PAS), the existing scheme (G).
Steiner and P.Schulte, "Bandwidth effectiveness and rate-modulated low-sensitivity pair-chemical modulation," in IEEE Transactions on Communications, vol.63, No.12, pp.4651-4665, dec.2015.), and (G.
Schulte and f. steiner, "basic mapping and forward error correction for fiber-optical communication systems," in Journal of light wave Technology, vol.37, No.2, pp.230-244, jan.15,2019.) joint coding of a Distribution Matcher (DM) with systematic binary low-density parity-check (LDPC) codes, in such joint coding schemes the complexity of the system depends mainly on the complexity of the DM. Many DM algorithms for high order qam signals are proposed, such as product Distribution Matching, hierarchical Distribution Matching, Constant Composition Distribution Matching (CCDM), m-out-of-n DM, and prefix-free Distribution Matching. Among them, CCDM is widely used due to near zero rate loss, but CCDM requires a long block length and high complexity. In contrast, with lower complexityCut-and-paste (CAP) based DM of (1) is promising in realizing PS-PAM signals. In CAP-based DM, the transmission sequence is divided into a number of n symbol segments, and for each n symbol segment, the amplitude bits are extracted and inverted after bit-to-symbol mapping. However, CAP-based DM requires more multipliers and comparators because two mappings are implemented to select sequences with lower energy. Furthermore, the sequences selected with lower energy always have a lower information rate and a certain distribution. In order to generate flexible probability distribution configurations, the existing scheme (m.liu, m.gao and j.ke, "Multi-distributed constrained symmetric PAM-4system for intra-data-center networks," chi.opt.let.vol.19, No.11, pp.110604, nov.2021.) proposes an Energy-level-allocation (ELA) -based DM for PS-PAM-4 signals by pre-calculating and allocating Energy levels. Therefore, the DM based on ELA is a simple method to realize the desired probability distribution, and is suitable for the PS-PAM-8 transmission system with lower complexity.
In addition, equalizers can mitigate Inter Symbol Interference (ISI), which is essential in PAM-8 transmissions. In general, a Feed-forward Equalizer (FFE) can effectively remove linear ISI, while a Volterra Equalizer (VE) can mitigate non-linear ISI. While both the feed forward equalizer and the Volterra equalizer can mitigate the power attenuation effects, they also add noise components. In addition, a Decision Feedback Equalizer (DFE) can compensate for the spectral notch caused by fiber dispersion, but its hard Decision module causes error propagation. Therefore, it is challenging to implement a cascade of DFE and FEC decoders. In contrast, Maximum Likelihood Sequence Estimation (MLSE) is typically combined with a feed forward equalizer and a volterra equalizer, which suppress noise through a post filter and utilize viterbi decoding to generate decision symbols. However, error propagation remains a pending problem in viterbi decoding of hard decision outputs. For this reason, some researchers have proposed MLSE algorithms with soft decisions for PAM-4 signaling (H.Rha, S.Moon, H.Kang, S.Lee, I.Hwang and J.Lee, "Low-complexity soft-decision Viterbi algorithm for IM/DD 56-Gb/s PAM-4system," in IEEE Photonics Technology Letters, vol.31, No.5, pp.361-364, Mar.1, 2019.). However, the computational complexity of MLSE grows exponentially, which brings difficulties for practical applications. In addition, in a bandwidth limited PAM system, Tomlinson-Harashima Precoding (THP) may be used to improve performance. However, THP cannot be applied directly to PS-PAM systems because the output signal of the nonlinear modulo operation in the feed-forward path of the precoder is somewhat random, thus destroying the Maxwell-Boltzmann (MB) distribution produced by the PS encoder.
In summary, the conventional PAM-8 optical interconnect system has the following problems: PAM-8 signals are susceptible to various linear and nonlinear noise from transceivers and transmission fibers, and conventional DM and equalizers used in long-distance optical communications are quite complex and not suitable for short-distance IM/DD PAM-8 signals.
Disclosure of Invention
Therefore, the invention provides a method and a system for short-distance transmission of a probability shaping PAM-8 signal to solve the existing technical problems, wherein a PS-PAM-8 signal with a better signal is obtained by adopting a joint coding mode of an ELA coder and an LDPC coder, so that the feasibility of the scheme is obviously improved, and the method and the system are suitable for short-distance IM/DD PAM-8 signal transmission.
In order to solve the technical problem, the invention provides a short-distance transmission method for probability shaping PAM-8 signals, which comprises the following steps:
deploying a PAS encoder at a transmitting end, receiving a transmitting signal from the transmitting end by the PAS encoder, carrying out encoding processing on the transmitting signal, mapping the encoded transmitting signal to generate a probability-shaped PS-PAM-8 symbol sequence, and transmitting the PS-PAM-8 symbol sequence through a channel, wherein the PAS encoder comprises an ELA encoder and an LDPC encoder, and the ELA encoder and the LDPC encoder are used for carrying out joint encoding;
the method comprises the steps of receiving a receiving signal at a receiving end, utilizing an equalizer arranged at the receiving end to recover the receiving signal to obtain a recovered PS-PAM-8 signal, decoding the recovered PS-PAM-8 signal by a PAS decoder arranged at the receiving end to obtain a transmitting signal sent by the sending end, wherein the equalizer comprises a feedforward equalizer, a 2-order Wal-Tyr equalizer and a 2-order simplified Wal-Tyr equalizer, the feedforward equalizer, the 2-order Wal-Tyr equalizer and the 2-order simplified Wal-Tyr equalizer are respectively used for processing the received receiving signal, and the 2-order simplified Wal-Tyr equalizer only keeps an inner core of the 2-order Wal-Tyr equalizer.
In one embodiment of the present invention, a method for joint encoding using the ELA encoder and the LDPC encoder includes:
receiving a transmission signal from a transmitting end by an ELA encoder, wherein the transmission signal comprises a first uniform random bit sequence, shaping the first uniform random bit sequence by using the ELA encoder, and outputting an amplitude bit sequence and a uniform label bit sequence;
receiving, by an LDPC encoder, a transmission signal from a transmitting end, wherein the transmission signal includes a second uniform random bit sequence, and the LDPC encoder is configured to generate a parity bit sequence, output the parity bit sequence with the received uniform tag bit sequence and the second uniform random bit sequence as symbol bits, and output an amplitude bit sequence.
In one embodiment of the invention, the method for generating the probability-shaped PS-PAM-8 symbol sequence by mapping the coded and processed transmission signal comprises the following steps:
and receiving the symbol bit and amplitude bit sequence, and mapping the symbol bit and amplitude bit sequence to generate a PS-PAM-8 symbol sequence.
In an embodiment of the present invention, a code rate R of the joint encoding performed by the ELA encoder and the LDPC encoder is represented as follows:
wherein 
And
respectively representing the entropy of amplitude bit and sign bit, H (A) representing the entropy of the amplitude after probability shaping, representing the ratio of sign bit carrying information, n c Representing the total number of symbols.
In one embodiment of the present invention, a method for decoding a recovered PS-PAM-8 signal by a PAS decoder includes:
the PAS decoder comprises a log-likelihood ratio calculation module, an LDPC decoder and an ELA decoder;
receiving a PS-PAM-8 receiving sequence generated after a PS-PAM-8 symbol sequence is transmitted through a channel by a log-likelihood ratio calculation module, and obtaining judgment information based on the PS-PAM-8 receiving sequence;
receiving decision information by an LDPC decoder, ordering the amplitude bit sequence and the uniform label bit sequence according to the decision information, outputting an estimated amplitude bit sequence and a uniform label bit sequence, and outputting an estimated second uniform random bit sequence;
and receiving the estimated amplitude bit sequence and the uniform label bit sequence by the ELA decoder, carrying out inverse operation on the estimated amplitude bit sequence and the uniform label bit sequence, and outputting an estimated first uniform random bit sequence.
In one embodiment of the present invention, the method in which the feedforward equalizer, the 2 nd-order Wal-tara equalizer, and the 2 nd-order simplified Wal-tara equalizer are used to process the received signal respectively comprises:
the expressions of the equalized signals d' (k) at the output of the feedforward equalizer, the 2 nd order Wal-tara equalizer and the 2 nd order simplified Wal-tara equalizer are:
d' FFE (k)＝W 01 Y 1
d' VE (k)＝W 01 Y 1 +W 02 Y 2
d' SVE (k)＝W 01 Y 1 +W 02 Y' 2
wherein ,W01 and W02 Is a vector of tap coefficients, Y 1 Is the input of a feedforward equalizer, Y 1 and Y2 Is the input of a 2 nd order Voltara equalizer, Y 1 and Y2' Is the input of a 2-stage simplified Volterra equalizer, Y 1 、Y 2 and Y2' The expression of (a) is as follows:
Y 1 ＝[y(k-N+1)…y(k)…y(k+N-1)]
Y 2 ＝[y 2 (k-M+1),y(k-M+1)y(k-M)…y(k-M+1)y(k+M-1)…y 2 (k),y(k)y(k+1)...y(k)y(k+M-1)…y 2 (k+M-1)]
Y' 2 ＝[y 2 (k-M+1)…y 2 (k)…y 2 (k+M-1)]
where y (k) is the k-th symbol received, N is the memory length of the feedforward equalizer, and M is the nonlinear memory length of the 2 nd order Waltera equalizer.
In addition, the invention also provides a probability shaping PAM-8 signal short-distance transmission system, which comprises:
the system comprises a PAS coding module, a data processing module and a data processing module, wherein the PAS coding module is used for deploying a PAS coder at a sending end, receiving a transmitting signal from the sending end by the PAS coder, coding the transmitting signal, mapping the coded transmitting signal to generate a probability-shaped PS-PAM-8 symbol sequence, and transmitting the PS-PAM-8 symbol sequence through a channel, wherein the PAS coder comprises an ELA coder and an LDPC coder and jointly codes by utilizing the ELA coder and the LDPC coder;
the PAS decoding module is used for receiving a receiving signal at a receiving end, recovering the receiving signal by utilizing an equalizer arranged at the receiving end to obtain a recovered PS-PAM-8 signal, and decoding the recovered PS-PAM-8 signal by utilizing a PAS decoder arranged at the receiving end to obtain a transmitting signal sent by the sending end, wherein the equalizer comprises a feedforward equalizer, a 2-order Wal-Tai equalizer and a 2-order simplified Wal-Tai equalizer, the feedforward equalizer, the 2-order Wal-Tai equalizer and the 2-order simplified Wal-Tai equalizer are respectively used for processing the received receiving signal, and the 2-order simplified Wal-Tai equalizer only keeps an inner core of the 2-order Wal-Tai equalizer.
In one embodiment of the present invention, the PAS encoder includes:
the ELA encoder is used for receiving a transmitting signal from a transmitting end, wherein the transmitting signal comprises a first uniform random bit sequence, the ELA encoder is used for shaping the first uniform random bit sequence, and an amplitude bit sequence and a uniform label bit sequence are output;
an LDPC encoder for receiving a transmission signal from a transmitting end, wherein the transmission signal includes a second uniform random bit sequence, and the LDPC encoder is for generating a parity bit sequence, outputting the parity bit sequence with the received uniform tag bit sequence and the second uniform random bit sequence as symbol bits, and for outputting an amplitude bit sequence.
In an embodiment of the present invention, a code rate R of the joint encoding performed by the ELA encoder and the LDPC encoder is represented as follows:
wherein ,
and
respectively representing the entropy of amplitude bit and sign bit, H (A) representing the entropy of the amplitude after probability shaping, gamma representing the ratio of sign bit carrying information, n c Representing the total number of symbols.
In one embodiment of the present invention, the PAS decoder includes:
the log-likelihood ratio calculation module is used for receiving a PS-PAM-8 receiving sequence generated after a PS-PAM-8 symbol sequence is transmitted through a channel and obtaining judgment information based on the PS-PAM-8 receiving sequence;
an LDPC decoder for receiving decision information, ordering the amplitude bit sequence and the uniform tag bit sequence according to the decision information, outputting an estimated amplitude bit sequence and a uniform tag bit sequence, and outputting an estimated second uniform random bit sequence;
and the ELA decoder is used for receiving the estimated amplitude bit sequence and the uniform label bit sequence, carrying out inverse operation on the estimated amplitude bit sequence and the uniform label bit sequence and outputting an estimated first uniform random bit sequence.
Compared with the prior art, the technical scheme of the invention has the following advantages:
the invention provides a probability shaping PAM-8 signal short-distance transmission method and a probability shaping PAM-8 signal short-distance transmission system, which adopt a mode of joint coding of an ELA coder and an LDPC coder to obtain a PS-PAM-8 signal with a better signal, obviously improve the feasibility of the scheme, further reduce the error rate at a receiving end by using a simplified equalizer, and obviously improve the receiving sensitivity in transmission, so that the probability shaping PAM-8 signal short-distance transmission method and the probability shaping PAM-8 signal short-distance transmission system can be suitable for short-distance IM/DD PAM-8 signal transmission.
Drawings
In order that the present disclosure may be more readily and clearly understood, reference is now made to the following detailed description of the embodiments of the present disclosure taken in conjunction with the accompanying drawings, in which
Fig. 1 is a block diagram of a PS-PAM-8 point-to-point transmission system in an IDC network of the present invention.
FIG. 2 is a diagram of the architecture of the PS-PAM-8 transmission system based on the joint coding of ELA and LDPC.
Fig. 3 is a schematic diagram of the symbol mapping rule of PAM-8.
Fig. 4 is a probability distribution histogram in which (a) represents a probability distribution histogram of PS-PAM-8, and (b) represents a probability distribution histogram of uniform PAM-8.
Fig. 5 is a schematic diagram of the equalizer structure of the present invention.
FIG. 6 is a graph of the measured BER for 20-GBaud PS-PAM-8 and 14.2-GBaud uniform PAM-8 signals.
FIG. 7 is a post-FEC BER curve and a post-ELA BER curve for a 2km SSMF transmission of a 20-GBaud PS-PAM-8 signal measured under different equalizers.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
First, the present invention makes the following explanations for english marks that need to appear hereinafter:
PS: probability shaping; and (4) DSP: processing a digital signal; FFE: a feed forward equalizer; VE: a Volterra equalizer; SVE: a simplified Volterra equalizer; PRBS: a pseudo-random binary sequence; AWG: an arbitrary waveform generator; MZM: a Mach modulator; SSMF: a standard single mode optical fiber; VOA: a variable optical attenuator; EDFA: an erbium-doped fiber amplifier; PD: a photodetector; RTO: a real-time oscilloscope; BTB: back to back; BER: bit error rate.
Example one
The following describes a short-distance transmission method for a probability shaping PAM-8 signal according to an embodiment of the present invention in detail.
The embodiment of the invention provides a short-distance transmission method for probability shaping PAM-8 signals, which comprises the following steps:
s10: deploying a PAS encoder at a transmitting end, receiving a transmitting signal from the transmitting end by the PAS encoder, carrying out encoding processing on the transmitting signal, mapping the encoded transmitting signal to generate a probability-shaped PS-PAM-8 symbol sequence, and transmitting the PS-PAM-8 symbol sequence through a channel, wherein the PAS encoder comprises an ELA encoder and an LDPC encoder, and the ELA encoder and the LDPC encoder are used for carrying out joint encoding;
s20: the method comprises the steps of receiving a receiving signal at a receiving end, utilizing an equalizer arranged at the receiving end to recover the receiving signal to obtain a recovered PS-PAM-8 signal, decoding the recovered PS-PAM-8 signal by a PAS decoder arranged at the receiving end to obtain a transmitting signal sent by the sending end, wherein the equalizer comprises a feedforward equalizer, a 2-order Wallace equalizer and a 2-order simplified Wallace equalizer, the feedforward equalizer, the 2-order Wallace equalizer and the 2-order simplified Wallace equalizer are respectively used for processing the received receiving signal, and the 2-order simplified Wallace equalizer only keeps an inner core of the 2-order Wallace equalizer.
To describe details of a short-distance transmission method of a probability shaping PAM-8 signal in more detail, please refer to fig. 1, which is a block diagram of a PS-PAM-8 point-to-point transmission system in an IDC network. At the transmitting end, a transmission signal, which may be a Pseudo-random Binary Sequence (PRBS), is first transmitted into a PAS encoder to generate a PS-PAM-8 Symbol Sequence, and then the PS-PAM-8 Symbol Sequence is up-sampled to 2 Samples Per Symbol (Samples Per Symbol, sps). Pulse shaping is then performed using a Root Raised Cosine (RRC) Finite Impulse Response (FIR) filter with a roll-off factor of 0.5. Next, a Pseudo-noise (PN) sequence is inserted to facilitate synchronization at the receiving end. Data processed by a sending end DSP is loaded into an Arbitrary Waveform Generator (AWG), the 3-dB bandwidth of the Generator is about 11GHz, the baud rate of a transmitting signal can be adjusted by changing the sampling rate of the AWG, and the maximum sampling rate of the AWG is 50 GS/s. Then, the PS-PAM-8 electrical signal is modulated into 1550.112nm Continuous Wave (CW) laser, and the power of the modulated PS-PAM-8 optical signal is about 5.7 dBm. Variable Optical Attenuators (VOAs) and Erbium-doped Fiber amplifiers (EDFAs) are used to control the noise level of BER measurements after transmission of an SSMF exceeding 2 km. The last VOA is used to adjust the optical power of the PD, where the PD has a 3dB bandwidth of 10-GHz. The signal after PD photoelectric conversion is collected by a Real-time Oscilloscope (RTO) with the sampling rate of 50-GS/s. The acquired signals are firstly processed by a synchronization algorithm to obtain signals synchronous with the transmitted signals. The signal is then resampled to 1sps and the received signal is obtained using matched filtering with the RRC FIR. Next, an equalizer is introduced to recover the received signal, resulting in a recovered PS-PAM-8 signal. Then, a decoding operation of the PAS decoder is performed to obtain a transmission signal of the transmitting end, which includes LLR calculation, LDPC decoder, and ELA decoder.
In the IM/DD PAM-8 system, symbols with higher amplitude levels always suffer more severe degradation. Thus, for a PS-PAM-8 signal, degradation is mitigated by reducing the probability of occurrence of symbols with higher amplitude levels and increasing the probability of occurrence of symbols with lower amplitude levels. In order to implement PAS generated by joint encoding of the ELA encoder and the LDPC encoder, an additional tag bit is required to indicate whether a bit is flipped. Errors in the tag bits will cause error propagation and it is therefore important to keep the tag bits undistorted. At the same time, the sign bit is less sensitive to noise during transmission. When the ELA coding is combined with the channel coding, the label bits generated by the ELA coding and the check bits generated by the LDPC coding can be transmitted as symbol bits, thereby ensuring the accuracy of the label bits and the check bits. Fig. 2 shows an architecture diagram of a PS-PAM-8 transmission system based on ELA and LDPC joint coding, which includes an ELA encoder, an LDPC encoder, a symbol mapping module, a transmission channel, a Log Likelihood Ratio (LLR) calculation module, an LDPC decoder, and an ELA decoder. Based on this, a first uniform random bit sequence U 1 Firstly, entering an ELA encoder to obtain a shaped amplitude bit sequence b (A) and a uniform label bit sequence L, wherein A represents a PS amplitude level sequence which only contains amplitude bit information. Each amplitude level in sequence a contains M-1 bits for each PAM-M symbol, M ═ log 2 (M). Thereafter, a second uniform random bit sequence U 2 Are sent to the LDPC encoder along with b, (a) and L. The parity bit sequence P, L and U generated by the LDPC encoder are then 2 Together as a symbol bit S in a PS-PAM-8 symbol, and a non-uniformly distributed amplitude bit sequence b (a) is output as an amplitude bit. And generating a symbol sequence X after passing through a PAM-8 symbol mapping module. Then, a receiving sequence Y is obtained after channel transmission. Then, soft decision information is obtained by LLR estimation, which is transmitted to the LDPC decoder. Then sorting the output bit sequence, sending the estimated amplitude bit sequence b (A) 'and L' to ELA decoder for inverse operation of DM to obtain estimated uniform bit sequence U 1' and U2 '。
Fig. 3 shows the symbol mapping rule for PAM-8, where the highest bit represents the sign bit and the lower two bits represent the magnitude bit. Next, a PS-PAM-8 signal is generated using the look-up table with a 2 symbol code in table 1. In an ELA encoder, the transmitted sequence is first divided into a number of 2 symbol groups. To avoid extensive calculations and comparisons of the original amplitude bit energies, the ELA encoder introduces energy levels into the look-up table. Here, the energies of various 2-symbol groups are calculated in advance and classified into different energy levels, and then an energy level mapping rule is assigned to generate a variable probability distribution. In table 1, one combination contains two amplitude bits of PAM-8 symbols, i.e. a 2-symbol code. For example, "0001" represents the amplitude of "7" and "5", and the amplitude bits are "00" and "01". U shape 1 Is the original uniform bit, and b (a) is the PS-coded bit. E 1 and E2 The energy representing the 2 symbol combination before and after ELA encoder is calculated in advance by the sum of the squared amplitudes of each symbol in the combination before encoding. L is a tag bit generated by ELA encoding, where "0" indicates a flip operation and "1" indicates no operation. The flip rule is "00" and "10", and "01" and "11" are interchanged. Here, it is prioritized to flip the combination having the higher energy level, and the uniformity of the tag bits must be ensured.
TABLE 1 PS-PAM-8 2 symbol combination lookup table
| U 1 | E 1 | b(A) | E 2 | L | U 1 | E 1 | b(A) | E 2 | L |
| 0000 | 98 | 1010 | 2 | 0 | 1000 | 50 | 0010 | 50 | 0 |
| 0001 | 74 | 1011 | 10 | 0 | 1001 | 26 | 1001 | 26 | 1 |
| 0010 | 50 | 1000 | 50 | 0 | 1010 | 2 | 1010 | 2 | 1 |
| 0011 | 58 | 1001 | 26 | 0 | 1011 | 10 | 1011 | 10 | 1 |
| 0100 | 74 | 1110 | 10 | 0 | 1100 | 58 | 0110 | 26 | 0 |
| 0101 | 50 | 1111 | 18 | 0 | 1101 | 34 | 1101 | 34 | 1 |
| 0110 | 26 | 0110 | 26 | 1 | 1110 | 10 | 1110 | 10 | 1 |
| 0111 | 34 | 0111 | 34 | 1 | 1111 | 18 | 1111 | 18 | 1 |
Fig. 4 shows a probability distribution histogram of a uniform PAM-8 signal and a PS-PAM-8 signal. The PS-PAM-8 signal exhibits an approximately bilateral MB distribution compared to the uniform amplitude distribution of uniform PAM-8. Since the PS signal improves transmission performance at the expense of reduced information entropy, it is generally desirable to keep the net bit rates of the PS signal and the uniform signal the same for a fair comparison. This can generally be achieved by increasing the baud rate of the PS signal. In the joint coding scheme, the code rate of each part is included, wherein the LDPC encoder contains 15% of coding redundancy. For ELA encoder, code rate R 1 ＝U 1 /(U 1 + L), for LPDC encoder, code rate R 2 ＝(U 1 +U 2 +L)/(U 1 +U 2 + L + P). Having information in PS-PAM-M signalsThe fraction gamma of the sign bit of information is equal to U 2 /(U 2 + L + P). Furthermore, the fraction γ of a uniform PAM-M signal is described as:
γ＝1-(1-R 2 )m (2-1)
wherein m is log 2 (M); the code rate R of the joint coding is expressed as:
wherein 
And
representing the entropy of the magnitude and sign bits, respectively, including n c Information of individual symbols, H (A) represents the amplitude entropy after probability shaping [11] . Furthermore, the net bit rate is obtained by multiplying the code rate R by the baud rate of the signal.
Although the PS-PAM-8 signal is more robust than a uniform PAM-8 signal due to its non-uniform amplitude distribution, an equalizer is still essential to remove its channel impairments. The channel damage short-distance IM/DD signal is mainly caused by factors such as limited device bandwidth, nonlinear distortion of a system, optical fiber dispersion and system noise. Here, bandwidth limitations typically result in power attenuation at higher frequencies, which is considered linear distortion. In contrast, nonlinear distortion comes mainly from the non-ideal transfer characteristics of the modulator and the square-law detection of the Photodetector (PD). The PAM signal received after PD detection can be written as,
where y (t) is the received signal, d c Is Direct Current (DC) bias, x (t) is the transmit signal, h (t) represents the channel response, and n (t) is the system noise. If the delay caused by the channel and the filter is not consideredLate, for the kth symbol, y (t) at time t ═ kT s The sampling values of (a) are:
wherein xk h (0) is the sample value of the kth symbol,
is the sum of the symbols at the kth sampling instant, except for the kth symbol. In equations 2-4, the first term is the dc component, the second term is the nonlinear distortion signal, the third term is the linear distortion signal, and the last term is the system noise. Therefore, it is necessary to apply an equalizer to remove the nonlinear and linear ISI caused by the second and third terms. The Volterra series model is widely applicable to a nonlinear system, the series expansion of the Volterra series model consists of a non-recursive series and can be described as follows:
where d (k) is the output of the equalizer, y (k) is the input of the equalizer, i.e. the signal after channel transmission, l i Is the memory length, w, of the ith Waltara equalizer 0i Are the tap coefficients of the ith order volterra equalizer. By adjusting the tap coefficients, the Waltera equalizer can mitigate linear ISI as well as high-order nonlinear ISI.
Fig. 5 shows a schematic diagram of an equalizer of the present invention, which includes a feed forward equalizer, a 2 nd order volterra equalizer and a 2 nd order simplified volterra equalizer, each of which is used to process a received signal, wherein the 2 nd order simplified volterra equalizer only retains the kernel of the 2 nd order volterra equalizer, which can reduce the complexity of the volterra equalizer. The feed forward equalizer includes only the upper half of the structure. In order to remove forward ISI and backward ISI, the effect of neighboring symbols on the current symbol must be considered.The input signal of the equalizer is different, wherein Y 1 Is the input of a feed-forward equalizer, Y 1 and Y2 Is the input of a 2 nd order Voltara equalizer, Y 1 and Y2' Is the input to a 2 nd order simplified volterra equalizer, which is defined as:
where y (k) is the k-th symbol received, N is the memory length of the feedforward equalizer, and M is the nonlinear memory length of the 2 nd order Waltz equalizer. The expression of the equalized signal d' (k) at the output of the feed forward equalizer, the 2 nd order Wal-tara equalizer and the 2 nd order simplified Wal-tara equalizer is
d' FFE (k)＝W 01 Y 1 (2-7)
d' VE (k)＝W 01 Y 1 +W 02 Y 2 (2-8)
d' SVE (k)＝W 01 Y 1 +W 02 Y' 2 (2-9)
wherein W01 and W02 Is a vector of tap coefficients. After the equalizer, training symbols are extracted to calculate the difference between the desired output and the actual output. The tap coefficients are then adjusted using a less complex NLMS algorithm and iterative training is performed to obtain the best tap coefficients until the MSE converges. Finally, the obtained tap coefficients are used for the received test symbols to obtain an equalized symbol sequence.
The invention provides a short-distance transmission method for a probability shaping PAM-8 signal, which adopts a mode of joint coding of an ELA coder and an LDPC coder to obtain a PS-PAM-8 signal with a better signal, thereby obviously improving the feasibility of the scheme, in addition, the error rate is further reduced by utilizing a simplified equalizer at a receiving end, the receiving sensitivity in the transmission can be obviously improved, and the method can be suitable for short-distance IM/DD PAM-8 signal transmission.
To further verify the beneficial effects of this embodiment, the method of the present invention implemented by the experimental apparatus based on the 20G-PS-PAM-8 transmission system shown in fig. 1 was compared with the error rate of the existing method in which the uniform PAM-8 signal was directly mapped without passing through the PAS encoder.
FIG. 6 plots the measured BER curves for a 20-GBaud PS-PAM-8 signal and a 14.2-GBaud uniform PAM-8 signal with the same net bit rate after use of a feed forward equalizer for BTB and 2-km SSMF transmissions. In the case of BTB, the post-FEC BER and post-ELA BER variation of the 20-GBaud PS-PAM-8 signal are represented by the curves marked with filled squares and open squares in FIG. 6, where ELA decoding performance is shown in the measurement of post-ELA BER, and from the curves, it can be seen that ELA decoding does not produce error propagation. Thus, joint encoding of ELA and LDPC guarantees accurate transmission of the tag bit sequence. The corresponding BER curves for the 20-GBaud PS-PAM-8 signal for a 2-km SSMF transmission are shown in FIG. 6 with the solid and open circle markers. It is clear that the signal impairments due to 2-km SSMF transmission are negligible. The post-FEC BER curves for 14.2G uniform PAM-8 signals with BTB and 2-km SSMF transmission are shown in FIG. 6 with solid and open five-pointed star labels. In summary, at the same net bit rate, PS-PAM-8 signals at high baud rates outperform uniform PAM-8 signals at low baud rates, where the impact of bandwidth limitations can be mitigated by PS. When the received optical power is-18 dBm, the 20-GBaud PS-PAM-8 signal is close to zero bit error, and the 14.2-GBaud uniform PAM-8 signal can realize zero bit error only when the received optical power is-17 dBm.
To compare the performance of various equalizers in a 2km SSMF transmission system, post-FEC BER and post-ELA BER curves for the 20-GBaud PS-PAM-8 signal were measured in fig. 7, with no error propagation observed, as shown by the solid and dashed curves. Similar to BTB transmission, a 2 nd order waltala equalizer and a 2 nd order simplified waltala equalizer can achieve better BER performance due to additional nonlinear equalization, as shown by the curves with circle, pentagram, and diamond marks in fig. 7. For lower Received Optical Power (ROP), the amplified spontaneous emission noise of EDFA dominates during noise loading in the system, and all equalizers have similar performance. As ROP increases, 2 nd order volterra equalizers and 2 nd order simplified volterra equalizers outperform feed forward equalizers, as shown in fig. 7. For longer SSMF transmissions, a higher order Waltera equalizer is essential to mitigate PAM-8 signal impairments. Although the signal attenuation is small in the 2km SSMF transmission, the received signal still contains 2-order nonlinear impairments, and the 2-order volterra equalizer and the 2-order simplified volterra equalizer can achieve better BER performance, as shown by the curves with the five-pointed star and the diamond marks in fig. 7. The 2-order simplified Waltera equalizer and the 2-order Waltera equalizer achieve error-free transmission performance in 20-GBaud PS-PAM-8BTB, introducing it into 2km SSMF transmission, the improvement in receiver sensitivity is reduced by about 1dB, since the damage caused by the optical fiber is not eliminated. Thus, a 2-order simplified Waltera equalizer is a better suited equalizer for PS-PAM-8 signals in networks within short-range data centers.
Example two
In the following, a probability shaping PAM-8 signal short-distance transmission system disclosed in the second embodiment of the present invention is introduced, and a probability shaping PAM-8 signal short-distance transmission system described below and a probability shaping PAM-8 signal short-distance transmission method described above may be referred to correspondingly.
The embodiment II of the invention discloses a probability shaping PAM-8 signal short-distance transmission system, which comprises:
the system comprises a PAS coding module, a data processing module and a data processing module, wherein the PAS coding module is used for deploying a PAS coder at a transmitting end, receiving a transmitting signal from the transmitting end by the PAS coder, coding the transmitting signal, mapping the coded transmitting signal to generate a probability-shaped PS-PAM-8 symbol sequence, and transmitting the PS-PAM-8 symbol sequence through a channel, wherein the PAS coder comprises an ELA coder and an LDPC coder and jointly codes by utilizing the ELA coder and the LDPC coder;
the PAS decoding module is used for receiving a receiving signal at a receiving end, recovering the receiving signal by utilizing an equalizer arranged at the receiving end to obtain a recovered PS-PAM-8 signal, and decoding the recovered PS-PAM-8 signal by utilizing a PAS decoder arranged at the receiving end to obtain a transmitting signal sent by the sending end, wherein the equalizer comprises a feedforward equalizer, a 2-order Wal-Tai equalizer and a 2-order simplified Wal-Tai equalizer, the feedforward equalizer, the 2-order Wal-Tai equalizer and the 2-order simplified Wal-Tai equalizer are respectively used for processing the received receiving signal, and the 2-order simplified Wal-Tai equalizer only keeps an inner core of the 2-order Wal-Tai equalizer.
In one embodiment of the present invention, the PAS encoder includes:
the ELA encoder is used for receiving a transmitting signal from a transmitting end, wherein the transmitting signal comprises a first uniform random bit sequence, the ELA encoder is used for shaping the first uniform random bit sequence, and an amplitude bit sequence and a uniform label bit sequence are output;
an LDPC encoder for receiving a transmission signal from a transmitting end, wherein the transmission signal includes a second uniform random bit sequence, and the LDPC encoder is for generating a parity bit sequence, outputting the parity bit sequence with the received uniform tag bit sequence and the second uniform random bit sequence as symbol bits, and for outputting an amplitude bit sequence.
In an embodiment of the present invention, a code rate R of the joint encoding performed by the ELA encoder and the LDPC encoder is represented as follows:
wherein ,
and
respectively representing the entropy of the amplitude bit and sign bit, H (A) representing the entropy of the probability-shaped amplitudeGamma denotes the sign bit ratio of the carried information, n c Representing the total number of symbols.
In one embodiment of the present invention, the PAS decoder includes:
the log-likelihood ratio calculation module is used for receiving a PS-PAM-8 receiving sequence generated after a PS-PAM-8 symbol sequence is transmitted through a channel and obtaining judgment information based on the PS-PAM-8 receiving sequence;
an LDPC decoder for receiving decision information, ordering the amplitude bit sequence and the uniform label bit sequence according to the decision information, outputting an estimated amplitude bit sequence and a uniform label bit sequence, and outputting an estimated second uniform random bit sequence;
and the ELA decoder is used for receiving the estimated amplitude bit sequence and the uniform label bit sequence, carrying out inverse operation on the estimated amplitude bit sequence and the uniform label bit sequence and outputting an estimated first uniform random bit sequence.
The probability shaping PAM-8 signal short-distance transmission system of the present embodiment is used to implement the foregoing probability shaping PAM-8 signal short-distance transmission method, and therefore, the specific implementation of the system can be seen in the foregoing section of the embodiment of the probability shaping PAM-8 signal short-distance transmission method, and therefore, the specific implementation thereof can refer to the description of the corresponding section embodiments, and will not be further described herein.
In addition, since the probability shaping PAM-8 signal short-distance transmission system of this embodiment is used to implement the foregoing probability shaping PAM-8 signal short-distance transmission method, its role corresponds to that of the foregoing method, and is not described here again.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. And obvious variations or modifications of the invention may be made without departing from the spirit or scope of the invention.
Claims (10)
1. A short-distance transmission method for probability shaping PAM-8 signals is characterized by comprising the following steps:
deploying a PAS encoder at a transmitting end, receiving a transmitting signal from the transmitting end by the PAS encoder, encoding the transmitting signal, mapping the encoded transmitting signal to generate a probability-shaped PS-PAM-8 symbol sequence, and transmitting the PS-PAM-8 symbol sequence through a channel, wherein the PAS encoder comprises an ELA encoder and an LDPC encoder, and joint encoding is performed by the ELA encoder and the LDPC encoder;
the method comprises the steps of receiving a receiving signal at a receiving end, utilizing an equalizer arranged at the receiving end to recover the receiving signal to obtain a recovered PS-PAM-8 signal, decoding the recovered PS-PAM-8 signal by a PAS decoder arranged at the receiving end to obtain a transmitting signal sent by the sending end, wherein the equalizer comprises a feedforward equalizer, a 2-order Wallace equalizer and a 2-order simplified Wallace equalizer, the feedforward equalizer, the 2-order Wallace equalizer and the 2-order simplified Wallace equalizer are respectively used for processing the received receiving signal, and the 2-order simplified Wallace equalizer only keeps an inner core of the 2-order Wallace equalizer.
2. The method for short-distance transmission of probability-shaped PAM-8 signals according to claim 1, wherein the method for joint encoding using the ELA encoder and LDPC encoder comprises:
receiving a transmission signal from a transmitting end by an ELA encoder, wherein the transmission signal comprises a first uniform random bit sequence, shaping the first uniform random bit sequence by using the ELA encoder, and outputting an amplitude bit sequence and a uniform label bit sequence;
receiving, by an LDPC encoder, a transmission signal from a transmitting end, wherein the transmission signal includes a second uniform random bit sequence, and the LDPC encoder is configured to generate a parity bit sequence, output the parity bit sequence with the received uniform tag bit sequence and the second uniform random bit sequence as symbol bits, and output an amplitude bit sequence.
3. The method for short-distance transmission of probability-shaped PAM-8 signals according to claim 2, wherein the method for generating probability-shaped PS-PAM-8 symbol sequences by mapping the encoded transmission signals comprises:
and receiving the symbol bit and amplitude bit sequence, and mapping the symbol bit and amplitude bit sequence to generate a PS-PAM-8 symbol sequence.
4. The method for short-distance transmission of probability-shaped PAM-8 signals according to claim 1 or 2, wherein the code rate R of the joint encoding by the ELA encoder and the LDPC encoder is represented as follows:
wherein ,
and
respectively representing the entropy of amplitude bit and sign bit, H (A) representing the entropy of the amplitude after probability shaping, gamma representing the ratio of sign bit carrying information, n c Representing the total number of symbols.
5. The method for short-distance transmission of probability-shaped PAM-8 signals according to claim 2, wherein the method for decoding the recovered PS-PAM-8 signals by a PAS decoder comprises:
the PAS decoder comprises a log-likelihood ratio calculation module, an LDPC decoder and an ELA decoder;
receiving a PS-PAM-8 receiving sequence generated after a PS-PAM-8 symbol sequence is transmitted through a channel by a log-likelihood ratio calculation module, and obtaining judgment information based on the PS-PAM-8 receiving sequence;
receiving decision information by an LDPC decoder, ordering the amplitude bit sequence and the uniform label bit sequence according to the decision information, outputting an estimated amplitude bit sequence and a uniform label bit sequence, and outputting an estimated second uniform random bit sequence;
and receiving the estimated amplitude bit sequence and the uniform label bit sequence by the ELA decoder, performing inverse operation on the estimated amplitude bit sequence and the uniform label bit sequence, and outputting an estimated first uniform random bit sequence.
6. The method for short range transmission of probability shaped PAM-8 signals according to claim 1, wherein the feed forward equalizer, 2-order volterra equalizer and 2-order simplified volterra equalizer are used to process the received signal respectively, comprising:
the expressions of the equalized signals d' (k) at the output of the feedforward equalizer, the 2 nd order Wal-tara equalizer and the 2 nd order simplified Wal-tara equalizer are:
d' FFE (k)＝W 01 Y 1
d' VE (k)＝W 01 Y 1 +W 02 Y 2
d' SVE (k)＝W 01 Y 1 +W 02 Y' 2
wherein ,W01 and W02 Is a vector of tap coefficients, Y 1 Is the input of a feedforward equalizer, Y 1 and Y2 Is the input of a 2-stage Voltalla equalizer, Y 1 and Y2' Is the input of a 2-stage simplified Voltara equalizer, Y 1 、Y 2 and Y2' The expression of (a) is as follows:
Y 1 ＝[y(k-N+1)…y(k)…y(k+N-1)]
Y 2 ＝[y 2 (k-M+1),y(k-M+1)y(k-M)…y(k-M+1)y(k+M-1)
…
y 2 (k),y(k)y(k+1)...y(k)y(k+M-1)
…
y 2 (k+M-1)]
Y′ 2 ＝[y 2 (k-M+1)…y 2 (k)…y 2 (k+M-1)]
where y (k) is the k-th symbol received, N is the memory length of the feed forward equalizer, and M is the nonlinear memory length of the 2 nd order Wallace equalizer.
7. A system for short-range transmission of probability-shaped PAM-8 signals, comprising:
the system comprises a PAS coding module, a data processing module and a data processing module, wherein the PAS coding module is used for deploying a PAS coder at a sending end, receiving a transmitting signal from the sending end by the PAS coder, coding the transmitting signal, mapping the coded transmitting signal to generate a probability-shaped PS-PAM-8 symbol sequence, and transmitting the PS-PAM-8 symbol sequence through a channel, wherein the PAS coder comprises an ELA coder and an LDPC coder and jointly codes by utilizing the ELA coder and the LDPC coder;
the PAS decoding module is used for receiving a receiving signal at a receiving end, recovering the receiving signal by utilizing an equalizer arranged at the receiving end to obtain a recovered PS-PAM-8 signal, and decoding the recovered PS-PAM-8 signal by utilizing a PAS decoder arranged at the receiving end to obtain a transmitting signal sent by the sending end, wherein the equalizer comprises a feedforward equalizer, a 2-order Wal-Tai equalizer and a 2-order simplified Wal-Tai equalizer, the feedforward equalizer, the 2-order Wal-Tai equalizer and the 2-order simplified Wal-Tai equalizer are respectively used for processing the received receiving signal, and the 2-order simplified Wal-Tai equalizer only keeps an inner core of the 2-order Wal-Tai equalizer.
8. The probability shaped PAM-8 signal short range transmission system of claim 7, wherein the PAS encoder comprises:
the ELA encoder is used for receiving a transmitting signal from a transmitting end, wherein the transmitting signal comprises a first uniform random bit sequence, the ELA encoder is used for shaping the first uniform random bit sequence, and an amplitude bit sequence and a uniform label bit sequence are output;
an LDPC encoder for receiving a transmission signal from a transmitting end, wherein the transmission signal includes a second uniform random bit sequence, and the LDPC encoder is for generating a parity bit sequence, outputting the parity bit sequence with the received uniform tag bit sequence and the second uniform random bit sequence as symbol bits, and for outputting an amplitude bit sequence.
9. The system for short-distance transmission of probability-shaped PAM-8 signals according to claim 8, wherein the code rate R of the joint encoding by the ELA encoder and LDPC encoder is represented as follows:
wherein ,
and
respectively representing the entropy of amplitude bit and sign bit, H (A) representing the entropy of the amplitude after probability shaping, gamma representing the ratio of sign bit carrying information, n c Representing the total number of symbols.
10. The probability shaped PAM-8 signal short range transmission system of claim 8, wherein the PAS decoder comprises:
the log-likelihood ratio calculation module is used for receiving a PS-PAM-8 receiving sequence generated after a PS-PAM-8 symbol sequence is transmitted through a channel and obtaining judgment information based on the PS-PAM-8 receiving sequence;
an LDPC decoder for receiving decision information, ordering the amplitude bit sequence and the uniform label bit sequence according to the decision information, outputting an estimated amplitude bit sequence and a uniform label bit sequence, and outputting an estimated second uniform random bit sequence;
and the ELA decoder is used for receiving the estimated amplitude bit sequence and the uniform label bit sequence, carrying out inverse operation on the estimated amplitude bit sequence and the uniform label bit sequence and outputting an estimated first uniform random bit sequence.
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