CN114938259B - 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 PAM-8 signal short distance transmission method of probability shaping, receive the transmitting signal and encode it by PAS encoder disposed on the sender, produce the symbol sequence after probability shaping, PAS encoder is encoded by ELA encoder and LDPC encoder jointly; and recovering the received signal received by the receiving end by using an equalizer to obtain a recovered signal, decoding the recovered signal by using a PAS decoder to obtain a transmitting signal, wherein the equalizer comprises a feedforward equalizer, a 2-order Volterra equalizer and a 2-order simplified Volterra equalizer, and the 2-order simplified Volterra equalizer only retains the kernel of the 2-order Volterra equalizer. The invention obtains the PS-PAM-8 signal with better signal by adopting the combined coding mode of the ELA coder and the LDPC coder, thereby obviously improving the feasibility of the scheme and being applicable to 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 probability shaping PAM-8 signal short-distance transmission method and system.
Background
In order to handle high capacity connections within a data center, an Intra-data-center (IDC) network requires low power consumption and low complexity high speed optical interconnect technology. The Intensity-modulated 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 have been widely studied.
Compared to PAM-4 signals, PAM-8 signals can carry more information, but at the cost of more complex digital signal processing (Digital Signal Processing, DSP). Furthermore, the robustness of the PAM-8 signal can be enhanced with a probabilistic shaping (Probabilistic 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 is superior to the uniform PAM-8 signal. Furthermore, the combination of PS and forward error correction (Forward Error Correction, FEC) can achieve Probabilistic amplitude shaping (Probabilitic Am)The project Shaping, PAS), the existing scheme (G. 
Steiner and P.Schultet, "Bandwidth efficient and rate-supported low-density property-check coded modulation," in IEEE Transactions on Communications, vol.63, no.12, pp.4651-4665, dec.2015) and (G.
Schulte and f.stepiner, "Probabilistic shaping and forward error correction for fiber-optic communication systems," in Journal of Lightwave Technology, vol.37, no.2, pp.230-244, jan.15, 2019.) jointly encodes a distribution matcher (Distribution Matcher, DM) with a systematic binary low density parity-check (LDPC) code, in which joint coding scheme the complexity of the system depends largely on the complexity of the DM. Many DM algorithms for higher order quadrature amplitude modulated signals have been proposed, such as product distribution matching, hierarchical distribution matching, constant component distribution matching (Constant Composition Distribution Matching, CCDM), m-out-of-n DM, prefix-free distribution matching, etc. Among them, CCDM is widely used due to near zero rate loss, but CCDM requires a long block length and is very complex. In contrast, cut-and-paste (CAP) -based DM with lower complexity is promising in implementing PS-PAM signals. In CAP-based DM, the transmission sequence is divided into a number of n symbol segments, for each of which amplitude bits are extracted and flipped 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 selected sequences with lower energy always have a lower information rate and a certain distribution. To generate a flexible probability distribution configuration, the prior art scheme (M.Liu, M.Gao and J.Ke, "Multi-distributed probabilistically shaped PAM-4 system for intra-data-center networks," chip. Opt. Lett. Vol.19, no.11, pp.110604, nov. 2021.) proposes an energy-based scheme for PS-PAM-4 signals by pre-computing and assigning energy levels Stage allocation (ELA) DM. Thus, ELA-based DM is a simple way to achieve the desired probability distribution, suitable for use in a low complexity PS-PAM-8 transmission system. />
In addition, the equalizer may mitigate inter-symbol interference (Inter Symbol Interference, ISI), which is essential in PAM-8 transmission. In general, a Feed-forward equalizer (Feed-forward Equalizer, FFE) can effectively cancel linear ISI, while a volterra equalizer (Volterra equalizer, VE) can mitigate nonlinear ISI. While both the feed forward equalizer and the waltay equalizer can mitigate the power attenuation effect, the noise component is also increased. In addition, decision feedback equalizer (Decision Feedback Equalizer, DFE) can compensate for spectral notch caused by fiber dispersion, but its hard decision module can cause error propagation. Thus, implementing a concatenation of DFE and FEC decoders is challenging. In contrast, maximum likelihood sequence estimation (Maximum Likelihood Sequence Estimation, MLSE) is typically combined with a feed forward equalizer and a volterra equalizer, which suppresses noise by a post-filter and utilizes viterbi decoding to produce decision symbols. However, error propagation remains a pending problem in viterbi decoding of hard decision outputs. To this end, a learner proposed an MLSE algorithm 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 makes practical use difficult. In addition, in bandwidth limited PAM systems, tomlinson-Harashima precoding (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 interconnection 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-range optical communications are quite complex and unsuitable for short-range IM/DD PAM-8 signals.
Disclosure of Invention
Therefore, in order to solve the technical problems, the invention provides a probability shaping PAM-8 signal short-distance transmission method and a system, which adopt a mode of combined coding of an ELA coder and an LDPC coder to obtain a PS-PAM-8 signal with better signal, thereby obviously improving the feasibility of the scheme and being suitable for short-distance IM/DD PAM-8 signal transmission.
In order to solve the technical problems, the invention provides a probability shaping PAM-8 signal short distance transmission method, which comprises the following steps:
a PAS encoder is deployed at a transmitting end, a transmitting signal from the transmitting end is received by the PAS encoder, the transmitting signal is subjected to coding processing, the coded transmitting signal is mapped to generate a PS-PAM-8 symbol sequence subjected to probability shaping, and the PS-PAM-8 symbol sequence is transmitted through a channel, wherein the PAS encoder comprises an ELA encoder and an LDPC encoder, and the ELA encoder and the LDPC encoder are utilized for joint coding;
And receiving a received signal at a receiving end, recovering the received signal by using an equalizer arranged at the receiving end to obtain a recovered PS-PAM-8 signal, and decoding the recovered PS-PAM-8 signal by using a PAS decoder arranged at the receiving end to obtain a transmitting signal transmitted by a transmitting end, wherein the equalizer comprises a feedforward equalizer, a 2-order Woltay equalizer and a 2-order simplified Woltay equalizer, and the feedforward equalizer, the 2-order Woltay equalizer and the 2-order simplified Woltay equalizer are respectively used for processing the received signal, wherein the 2-order simplified Woltay equalizer only retains the kernel of the 2-order Woltay 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, and shaping the first uniform random bit sequence by the ELA encoder to output an amplitude bit sequence and a uniform tag bit sequence;
a transmit signal from a transmitting end is received by an LDPC encoder, wherein the transmit 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 sign bits, and output an amplitude bit sequence.
In one embodiment of the present invention, a method for generating a probability-shaped PS-PAM-8 symbol sequence from a coded transmission signal by mapping includes:
and receiving the symbol bit and the amplitude bit sequence, and mapping the symbol bit and the amplitude bit sequence to generate the PS-PAM-8 symbol sequence.
In one embodiment of the present invention, the code rate R of the joint encoding by the ELA encoder and the LDPC encoder is represented as follows:
wherein 
and />
Entropy of amplitude bit and sign bit respectively, H (A) represents the amplitude entropy after probability shaping, represents the sign bit duty ratio carrying information, n c Representing the total number of symbols.
In one embodiment of the present invention, a method for decoding a restored 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;
a log-likelihood ratio calculation module receives a PS-PAM-8 receiving sequence generated after a PS-PAM-8 symbol sequence is transmitted through a channel, and decision information is obtained based on the PS-PAM-8 receiving sequence;
receiving decision information by the LDPC decoder, 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;
The estimated amplitude bit sequence and the uniform tag bit sequence are received by an ELA decoder and are inverse operated to output 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 volterra equalizer, and the 2 nd order reduced volterra equalizer are respectively used to process the received signal includes:
the expression of the equalizing signals d' (k) at the output ends of the feedforward equalizer, the 2-order volterra equalizer and the 2-order simplified volterra equalizer is as follows:
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 the vector of tap coefficients, Y 1 Is the input of the feedforward equalizer, Y 1 and Y2 Is the input of the 2 nd order Wolta equalizer, Y 1 and Y2' Is the input of a 2 nd order reduced Walter equalizer, Y 1 、Y 2 and Y2' The expression of (2) 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 received kth symbol, N is the memory length of the feedforward equalizer, and M is the nonlinear memory length of the 2 nd order Wolta equalizer.
In addition, the invention also provides a probability shaping PAM-8 signal short distance transmission system, which comprises:
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 PS-PAM-8 symbol sequence subjected to probability shaping, and transmitting the PS-PAM-8 symbol sequence through a channel, wherein the PAS coder comprises an ELA coder and an LDPC coder, and the ELA coder and the LDPC coder are utilized for joint coding;
And the PAS decoding module is used for receiving a received signal at a receiving end, recovering the received 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 a PAS decoder arranged at the receiving end to obtain a transmitting signal transmitted by a transmitting end, wherein the equalizer comprises a feedforward equalizer, a 2-order Woltay equalizer and a 2-order simplified Woltay equalizer, and the feedforward equalizer, the 2-order Woltay equalizer and the 2-order simplified Woltay equalizer are respectively used for processing the received signal, wherein the 2-order simplified Woltay equalizer only retains the kernel of the 2-order Woltay equalizer.
In one embodiment of the present invention, the PAS encoder includes:
an ELA encoder for receiving a transmission signal from a transmitting end, wherein the transmission signal includes a first uniform random bit sequence, shaping the first uniform random bit sequence with the ELA encoder, and outputting an amplitude bit sequence and a uniform tag bit sequence;
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 second uniform random bit sequence as sign bits, and outputting an amplitude bit sequence.
In one embodiment of the present invention, the code rate R of the joint encoding by the ELA encoder and the LDPC encoder is represented as follows:
wherein ,
and />
Entropy of amplitude bit and sign bit respectively, H (A) represents amplitude entropy after probability shaping, gamma represents sign bit duty ratio 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 the 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, performing 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 system, which adopt an ELA encoder and LDPC encoder combined encoding mode to obtain a PS-PAM-8 signal with better signal, thereby obviously improving the feasibility of the scheme.
Drawings
In order that the invention may be more readily understood, a more particular description of the invention will be rendered by reference to specific embodiments thereof that are illustrated in the appended drawings, in which
Fig. 1 is a block diagram of a PS-PAM-8 point-to-point transmission system in an IDC network according to the present invention.
Fig. 2 is a diagram of a PS-PAM-8 transmission system architecture based on ELA and LDPC joint coding in accordance with the present invention.
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 of the present invention.
FIG. 6 is a BER curve of the measured 20-GBaud PS-PAM-8 and 14.2-GBaud uniform PAM-8 signals.
FIG. 7 is a post-FEC BER curve and post-ELA BER curve of a 20-GBaud PS-PAM-8 signal 2km SSMF transmission measured at different equalizers.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and specific examples, which are not intended to be limiting, so that those skilled in the art will better understand the invention and practice it.
Firstly, the invention makes the following definitions for English marks which need to appear in the following:
PS: probability shaping; DSP: digital signal processing; FFE: a feedforward equalizer; VE: a volterra equalizer; SVE: a simplified waltay equalizer; PRBS: a pseudo-random binary sequence; AWG: an arbitrary waveform generator; MZM: a Mach-Zehnder 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 1
The following describes a short-distance transmission method for a probability shaping PAM-8 signal in detail.
The embodiment of the invention provides a probability shaping PAM-8 signal short-distance transmission method, which comprises the following steps:
s10: a PAS encoder is deployed at a transmitting end, a transmitting signal from the transmitting end is received by the PAS encoder, the transmitting signal is subjected to coding processing, the coded transmitting signal is mapped to generate a PS-PAM-8 symbol sequence subjected to probability shaping, and the PS-PAM-8 symbol sequence is transmitted through a channel, wherein the PAS encoder comprises an ELA encoder and an LDPC encoder, and the ELA encoder and the LDPC encoder are utilized for joint coding;
S20: and receiving a received signal at a receiving end, recovering the received signal by using an equalizer arranged at the receiving end to obtain a recovered PS-PAM-8 signal, and decoding the recovered PS-PAM-8 signal by using a PAS decoder arranged at the receiving end to obtain a transmitting signal transmitted by a transmitting end, wherein the equalizer comprises a feedforward equalizer, a 2-order Woltay equalizer and a 2-order simplified Woltay equalizer, and the feedforward equalizer, the 2-order Woltay equalizer and the 2-order simplified Woltay equalizer are respectively used for processing the received signal, wherein the 2-order simplified Woltay equalizer only retains the kernel of the 2-order Woltay equalizer.
For a more detailed description of a short-range transmission method for probability-shaped PAM-8 signals, please refer to fig. 1, fig. 1 is a block diagram of a PS-PAM-8 point-to-point transmission system in an IDC network. At the transmitting end, the 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, which is then up-sampled to 2 samples per symbol (Samples Per Symbol, sps). Pulse shaping is then performed using a root raised cosine (Root Raised Cosine, RRC) finite impulse response (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. The data processed by the transmitting DSP is loaded into an arbitrary waveform generator (Arbitrary Wave form Generator, AWG) having a 3-dB bandwidth of approximately 11GHz, the baud rate of the transmitted signal being adjustable by varying the sampling rate of the AWG, wherein the maximum sampling rate of the AWG is 50GS/s. Then, the PS-PAM-8 electric signal is modulated into a 1550.112nm Continuous Wave (CW) laser, and the power of the modulated PS-PAM-8 optical signal is about 5.7dBm. Variable optical attenuators (Variable Optical Attenuator, VOA) and Erbium-doped fiber amplifiers (Erbium-doped Fiber Amplifier, EDFA) are used to control the noise level of BER measurements after transmission beyond 2km SSMF. The last VOA is used to adjust the optical power of the PD, which has a 3dB bandwidth of 10-GHz. The PD photoelectric converted signal is collected by a Real-time oscilloscope (Real-time Oscilloscope, RTO) with the sampling rate of 50-GS/s. The acquired signals are processed by a synchronization algorithm to obtain signals synchronized with the transmitted signals. Thereafter, the signal is resampled to 1sps and matched filtered using RRC FIR to obtain the received signal. 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 IM/DD PAM-8 systems, symbols with higher amplitude levels always suffer from more severe degradation. Thus, for the PS-PAM-8 signal, degradation is mitigated by reducing the probability of occurrence of symbols having higher amplitude levels and increasing the probability of occurrence of symbols having lower amplitude levels. In order to implement PAS generated by the ELA encoder and the LDPC encoder joint encoding, additional tag bits are required to indicate whether the bits are flipped. Errors in the tag bits will cause error propagation and thus it is important to keep the tag bits undistorted. At the same time, the sign bit is less sensitive to noise during transmission. When ELA coding is combined with channel coding, the tag bits generated by ELA coding and the check bits generated by LDPC codingCan be transmitted as sign bits, thereby ensuring the accuracy of the tag bits and the check bits. Fig. 2 shows a PS-PAM-8 transmission system architecture diagram 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 (Log Likelihood Ratio, LLR) calculation module, an LDPC decoder, and an ELA decoder. Based on this, a first uniform random bit sequence U 1 The ELA encoder is first entered to obtain a shaped amplitude bit sequence b (a) and a uniform tag bit sequence L, where a represents a PS-back amplitude level sequence containing only amplitude bit information. For each PAM-M symbol, each amplitude level in sequence a contains M-1 bits, m=log 2 (M). Thereafter, a second uniform random bit sequence U 2 Is transmitted to the LDPC encoder together with b (a) and L. Parity bit sequence P, L and U generated by LDPC encoder 2 Together as sign bits S in the PS-PAM-8 sign, the unevenly distributed amplitude bit sequence b (a) is output as amplitude bits. And generating a symbol sequence X after passing through a PAM-8 symbol mapping module. Then, the reception sequence Y is obtained after channel transmission. Then, soft decision information is obtained through LLR estimation, and the information is transmitted to the LDPC decoder. The output bit sequence is then ordered, and the estimated amplitude bit sequences b (A) 'and L' are sent to an ELA decoder for the inverse operation of DM to obtain an estimated uniform bit sequence U 1' and U2 '。
Fig. 3 shows the symbol mapping rule of PAM-8, wherein the most significant bit represents the symbol bit and the lower two bits represent the amplitude bit. Next, a look-up table with a 2 symbol code in table 1 is used to generate the PS-PAM-8 signal. In an ELA encoder, the transmitted sequence is first divided into a number of 2 symbol groups. To avoid extensive computation and comparison of the original amplitude bit energy, 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 PAM-8 symbol amplitude bits, i.e. 2 symbol coding. For example, "0001" means the magnitudes of "7" and "5" with the magnitude bits being "00" and "01". U (U) 1 Is the original uniform bit and b (a) is the PS encoded bit. E (E) 1 and E2 The energy representing the combination of 2 symbols before and after the ELA encoder is calculated in advance by summing the square of the magnitudes 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 flipping rule is "00" and "10", and "01" and "11" are interchanged. Here, it is prioritized that the combination with the higher energy level is flipped, and uniformity of the tag bit 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 probability distribution histograms of uniform PAM-8 signal and PS-PAM-8 signal. The PS-PAM-8 signal exhibits approximately a bilateral MB distribution compared to the uniform amplitude distribution of uniform PAM-8. Since PS signals improve transmission performance at the cost of reduced information entropy, it is often desirable to keep the net bit rate of PS signals and uniform signals the same for fair comparison. This can generally be achieved by increasing the baud rate of PS signals. In the joint coding scheme, the code rate of each part is included, wherein the LDPC encoder contains 15% coding redundancy. For ELA encoder, code rate R 1 ＝U 1 /(U 1 +L), code rate R for LPDC encoder 2 ＝(U 1 +U 2 +L)/(U 1 +U 2 +l+p). The fraction of sign bits with information in PS-PAM-M signal γ=u 2 /(U 2 +l+p). Furthermore, the fraction γ of the uniform PAM-M signal is described as:
γ＝1-(1-R 2 )m (2-1)
where m=log 2 (M); the code rate R of joint coding is expressed as:
wherein 
and />
Entropy representing amplitude bits and sign bits, respectively, comprising n c Information of each symbol, H (A) represents 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 eliminate its channel impairments. The channel impairment short-range IM/DD signal is mainly caused by factors such as limited device bandwidth, nonlinear system distortion, fiber dispersion, and system noise. Here, bandwidth limitations typically result in higher frequency power attenuation, which is considered linear distortion. In contrast, nonlinear distortion is mainly derived from non-ideal transfer characteristics of modulators and square law detection of Photodetectors (PDs). The PAM signal received after PD detection can be written as,
where y (t) is the received signal, d c Is a dc (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 delays caused by the channel and the filter are not taken into account, y (t) is at time t=kt for the kth symbol s The sampled values of (2) are:
wherein xk h (0) is the sample value of the kth symbol,
is the sum of the symbols other than the kth symbol at the kth sampling instant. 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. Thus, an equalizer is applied to cancel the signal generated byThe non-linearity and linearity ISI caused by the second and third term are very necessary. The Volterra series model is widely applicable to nonlinear systems, and the series expansion thereof consists of a non-recursive series, which can be described as:
where d (k) is the equalizer output, y (k) is the equalizer input, i.e. the signal after channel transmission, l i Is the memory length, w, of the ith order Wolta equalizer 0i Is the tap coefficient of the i-th order volterra equalizer. By adjusting the tap coefficients, the volterra equalizer can mitigate linear ISI as well as higher order nonlinear ISI.
Fig. 5 shows a schematic diagram of the equalizer structure of the present invention, which includes a feedforward equalizer, a 2-order volterra equalizer, and a 2-order simplified volterra equalizer, which are used to process received signals, respectively, wherein the 2-order simplified volterra equalizer retains only the kernel of the 2-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 cancel the forward ISI and the backward ISI, the influence of adjacent symbols on the current symbol must be considered. The equalizer has different input signals, wherein Y 1 Is the input of the feedforward equalizer, Y 1 and Y2 Is the input of the 2 nd order Wolta equalizer, Y 1 and Y2' Is the input of a 2 nd order reduced volterra equalizer, defined as:
where y (k) is the kth symbol received, N is the memory length of the feedforward equalizer, and M is the nonlinear memory length of the 2 nd order volterra equalizer. The expression of the equalized signal d' (k) at the output of the feedforward equalizer, the 2 nd order volterra equalizer and the 2 nd order reduced volterra 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 probability shaping PAM-8 signal short distance transmission method, which adopts an ELA encoder and LDPC encoder combined encoding mode to obtain a PS-PAM-8 signal with better signal, thereby obviously improving the feasibility of the scheme.
In order to further verify the beneficial effects of the present embodiment, the error rate comparison will be performed by using the method of the present invention implemented based on the experimental apparatus of the 20G-PS-PAM-8 transmission system shown in fig. 1 and the existing method in which the uniform PAM-8 signal is directly mapped without passing through the PAS encoder.
Fig. 6 plots the measured BER curves of the 20-GBaud PS-PAM-8 signal and the 14.2-GBaud uniform PAM-8 signal with the same net bit rate as a function of received optical power after using a feedforward equalizer in case of BTB and 2-km SSMF transmission. In the case of BTB, the post-FEC BER and post-ELA BER changes for the 20-GBaud PS-PAM-8 signal are represented by the solid square and open square marked curves in fig. 6, where ELA decoding performance is reflected in the measurement of post-ELA BER, from which it can be seen that ELA decoding does not produce error propagation. Thus, the joint encoding of ELA and LDPC ensures accurate transmission of the tag bit sequence. The corresponding BER curves for the 20-GBaud PS-PAM-8 signal transmitted by the 2-km SSMF are shown in FIG. 6 with filled and open circle marks. It is apparent that the signal impairments caused by the 2-km SSMF transmission are negligible. The post-FEC BER curve for a 14.2G uniform PAM-8 signal with BTB and 2-km SSMF transmission is shown in FIG. 6 with solid and open pentagram labels. In summary, at the same net bit rate, the performance of the high baud rate PS-PAM-8 signal is better than the low baud rate uniform PAM-8 signal, where the impact of bandwidth limitations can be mitigated by the PS. The 20-GBaud PS-PAM-8 signal approaches zero error code when the received optical power is-18 dBm, and the 14.2-GBaud uniform PAM-8 signal can realize zero error code 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, which were shown with no error propagation observed, as solid and dashed curves. Similar to BTB transmissions, a 2 nd order volterra equalizer and a 2 nd order reduced volterra equalizer may achieve better BER performance due to additional nonlinear equalization, as shown by the rounded, pentagram, and diamond marked curves in fig. 7. For lower received optical powers (Received Optical Power, ROP), the system dominates the amplified spontaneous emission noise of the EDFA during noise loading, and all equalizers have similar performance. As ROP increases, the 2 nd order volterra equalizer and the 2 nd order reduced volterra equalizer are superior to the feed forward equalizer, as shown in fig. 7. For longer SSMF transmissions, higher order waltay equalizers are essential to mitigate PAM-8 signal impairments. Although the signal attenuation is small in 2km SSMF transmission, the received signal still contains 2 nd order nonlinear impairments, and the 2 nd order volterra equalizer and the 2 nd order reduced volterra equalizer can achieve better BER performance, as shown by the curves with pentagram and diamond marks in fig. 7. The 2-order simplified volterra equalizer and the 2-order volterra equalizer realize error-free transmission performance in 20-GBaud PS-PAM-8BTB, and introduce it into 2km SSMF transmission, the improvement of receiver sensitivity is reduced by about 1dB, because the damage caused by the optical fiber is not eliminated. Therefore, the 2-order reduced Woltah equalizer is an equalizer that is more suitable for PS-PAM-8 signals in a network within a short-range data center.
Example two
The following describes a probability shaping PAM-8 signal short-range transmission system disclosed in the second embodiment of the present invention, and the probability shaping PAM-8 signal short-range transmission system described in the following and the probability shaping PAM-8 signal short-range transmission method described in the foregoing may be referred to correspondingly.
The second embodiment of the invention discloses a probability shaping PAM-8 signal short distance transmission system, which comprises:
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 PS-PAM-8 symbol sequence subjected to probability shaping, and transmitting the PS-PAM-8 symbol sequence through a channel, wherein the PAS coder comprises an ELA coder and an LDPC coder, and the ELA coder and the LDPC coder are utilized for joint coding;
and the PAS decoding module is used for receiving a received signal at a receiving end, recovering the received 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 a PAS decoder arranged at the receiving end to obtain a transmitting signal transmitted by a transmitting end, wherein the equalizer comprises a feedforward equalizer, a 2-order Woltay equalizer and a 2-order simplified Woltay equalizer, and the feedforward equalizer, the 2-order Woltay equalizer and the 2-order simplified Woltay equalizer are respectively used for processing the received signal, wherein the 2-order simplified Woltay equalizer only retains the kernel of the 2-order Woltay equalizer.
In one embodiment of the present invention, the PAS encoder includes:
an ELA encoder for receiving a transmission signal from a transmitting end, wherein the transmission signal includes a first uniform random bit sequence, shaping the first uniform random bit sequence with the ELA encoder, and outputting an amplitude bit sequence and a uniform tag bit sequence;
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 second uniform random bit sequence as sign bits, and outputting an amplitude bit sequence.
In one embodiment of the present invention, the code rate R of the joint encoding by the ELA encoder and the LDPC encoder is represented as follows:
wherein ,
and />
Entropy of amplitude bit and sign bit respectively, H (A) represents amplitude entropy after probability shaping, gamma represents sign bit duty ratio 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 the 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, performing 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-range transmission system of this embodiment is used to implement the foregoing probability shaping PAM-8 signal short-range transmission method, so that the detailed description of the system can be found in the foregoing example section of the probability shaping PAM-8 signal short-range transmission method, and therefore, the detailed description of the system can be referred to the corresponding description of the examples of the various sections, and will not be further described herein.
In addition, since the probability shaping PAM-8 signal short-range transmission system of the present embodiment is used to implement the foregoing probability shaping PAM-8 signal short-range transmission method, the function thereof corresponds to the function of the foregoing method, and will not be described herein.
It will be appreciated by those skilled in the art that 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 flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations 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 is apparent that the above examples are given by way of illustration only and are not limiting of the embodiments. Other variations and modifications of the present invention will be apparent to those of ordinary skill in the art in light of the foregoing description. It is not necessary here nor is it exhaustive of all embodiments. And obvious variations or modifications thereof are contemplated as falling within the scope of the present invention.
Claims (5)
1. A method for probability shaping PAM-8 signal short-range transmission, comprising:
a PAS encoder is deployed at a transmitting end, a transmitting signal from the transmitting end is received by the PAS encoder, the transmitting signal is subjected to coding processing, the coded transmitting signal is mapped to generate a PS-PAM-8 symbol sequence subjected to probability shaping, and the PS-PAM-8 symbol sequence is transmitted through a channel, wherein the PAS encoder comprises an ELA encoder and an LDPC encoder, and the ELA encoder and the LDPC encoder are utilized for joint coding;
receiving a receiving signal at a receiving end, recovering the receiving signal by using an equalizer arranged at the receiving end to obtain a recovered PS-PAM-8 signal, and decoding the recovered PS-PAM-8 signal by a PAS decoder arranged at the receiving end to obtain a transmitting signal transmitted by a transmitting end, wherein the equalizer comprises a feedforward equalizer, a 2-order Woltala equalizer and a 2-order simplified Woltala equalizer, and the feedforward equalizer, the 2-order Woltala equalizer and the 2-order simplified Woltala equalizer are respectively used for processing the received signal, wherein the 2-order simplified Woltala equalizer only retains the kernel of the 2-order Woltala equalizer;
The method for performing joint coding by using the ELA encoder and the LDPC encoder comprises the following steps:
receiving a transmission signal from a transmitting end by an ELA encoder, wherein the transmission signal comprises a first uniform random bit sequence, and shaping the first uniform random bit sequence by the ELA encoder to output an amplitude bit sequence and a uniform tag 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 sign bits, and output an amplitude bit sequence; the code rate R of the joint coding by the ELA encoder and the LDPC encoder is expressed as follows:
wherein ,
and />
Entropy of amplitude bit and sign bit respectively, H (A) represents amplitude entropy after probability shaping, gamma represents sign bit duty ratio carrying information, n c Representing the total number of symbols;
the method in which the feedforward equalizer, the 2 nd-order volterra equalizer, and the 2 nd-order reduced volterra equalizer are respectively used to process the received signal includes:
The expression of the equalizing signals d' (k) at the output ends of the feedforward equalizer, the 2-order volterra equalizer and the 2-order simplified volterra equalizer is as follows:
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 the vector of tap coefficients, Y 1 Is the input of the feedforward equalizer, Y 1 and Y2 Is the input of the 2 nd order Wolta equalizer, Y 1 and Y′2 Is the input of a 2 nd order reduced Walter equalizer, Y 1 、Y 2 and Y′2 The expression of (2) 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 received kth symbol, N is the memory length of the feedforward equalizer, and M is the nonlinear memory length of the 2 nd order Wolta equalizer.
2. The method for short-range transmission of a probability-shaped PAM-8 signal according to claim 1, wherein the method for generating a probability-shaped PS-PAM-8 symbol sequence from the encoded transmission signal by mapping comprises:
and receiving the symbol bit and the amplitude bit sequence, and mapping the symbol bit and the amplitude bit sequence to generate the PS-PAM-8 symbol sequence.
3. The probability shaping PAM-8 signal short distance transmission method of claim 1, wherein the decoding process of the recovered PS-PAM-8 signal by the PAS decoder comprises:
the PAS decoder comprises a log-likelihood ratio calculation module, an LDPC decoder and an ELA decoder;
A log-likelihood ratio calculation module receives a PS-PAM-8 receiving sequence generated after a PS-PAM-8 symbol sequence is transmitted through a channel, and decision information is obtained based on the PS-PAM-8 receiving sequence;
receiving decision information by the LDPC decoder, 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;
the estimated amplitude bit sequence and the uniform tag bit sequence are received by an ELA decoder and are inverse operated to output an estimated first uniform random bit sequence.
4. A probability shaping PAM-8 signal short range transmission system comprising:
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 PS-PAM-8 symbol sequence subjected to probability shaping, and transmitting the PS-PAM-8 symbol sequence through a channel, wherein the PAS coder comprises an ELA coder and an LDPC coder, and the ELA coder and the LDPC coder are utilized for joint coding;
The PAS decoding module is used for receiving a received signal at a receiving end, recovering the received 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 a PAS decoder arranged at the receiving end to obtain a transmitting signal transmitted by a transmitting end, wherein the equalizer comprises a feedforward equalizer, a 2-order Woltay equalizer and a 2-order simplified Woltay equalizer, and the feedforward equalizer, the 2-order Woltay equalizer and the 2-order simplified Woltay equalizer are respectively used for processing the received signal, wherein the 2-order simplified Woltay equalizer only retains the kernel of the 2-order Woltay equalizer;
the PAS encoder includes:
an ELA encoder for receiving a transmission signal from a transmitting end, wherein the transmission signal includes a first uniform random bit sequence, shaping the first uniform random bit sequence with the ELA encoder, and outputting an amplitude bit sequence and a uniform tag bit sequence;
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 second uniform random bit sequence as sign bits, and outputting an amplitude bit sequence; the code rate R of the joint coding by the ELA encoder and the LDPC encoder is expressed as follows:
wherein ,
and />
Entropy of amplitude bit and sign bit respectively, H (A) represents amplitude entropy after probability shaping, gamma represents sign bit duty ratio carrying information, n c Representing the total number of symbols; the feedforward equalizer, the 2-order Woltah equalizer and the 2-order simplified Woltah equalizer are respectively used for processing received signalsThe method for receiving the signal comprises the following steps:
the expression of the equalizing signals d' (k) at the output ends of the feedforward equalizer, the 2-order volterra equalizer and the 2-order simplified volterra equalizer is as follows:
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 the vector of tap coefficients, Y 1 Is the input of the feedforward equalizer, Y 1 and Y2 Is the input of the 2 nd order Wolta equalizer, Y 1 and Y′2 Is the input of a 2 nd order reduced Walter equalizer, Y 1 、Y 2 and Y′2 The expression of (2) 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 received kth symbol, N is the memory length of the feedforward equalizer, and M is the nonlinear memory length of the 2 nd order Wolta equalizer.
5. The probability shaping PAM-8 signal short range transmission system of claim 4, wherein said PAS decoder comprises:
the log-likelihood ratio calculation module is used for receiving a PS-PAM-8 receiving sequence generated after the 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, performing 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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