A Decoding Method of LDPC Codes Based on Neural Networks in an Optical Fiber Communication System

Abstract

The present invention discloses a decoding method for LDPC codes based on neural networks in an optical fiber communication system. In order to mitigate the influence of short cycles in the iterative decoding process, the present invention adds weights and biases considering the characteristics of the optical link to the edges corresponding to the variable node to check node update equation of the NOMS algorithm, thereby improving the decoding performance. The present invention utilizes the quasi-cyclic structure of QC-LDPC codes, and the same parameters are shared among a bunch of edges derived from the same edge of the exponent matrix. Compared with the traditional NOMS algorithm, the present invention can bring a certain signal-to-noise ratio gain in the optical fiber communication link, and the trained parameters have strong generalization ability.

Description

Technical Field

[0001] The present invention belongs to the field of communication technologies, relates to the key technologies of LDPC codes, and particularly relates to a method for decoding LDPC codes based on a neural network in an optical fiber communication system. Background Art

[0002] Since the forward error correction (FEC) technology was first proposed in the early 1990s, many types of codewords have been used in optical fiber communication systems to handle optical impairments such as uncompensated dispersion, polarization mode dispersion, and non-linear effects, and to keep the bit error rate (BER) at a sufficiently low level over long distances. In recent years, with the rapid development of microelectronics technology, people have conducted in-depth research on the iterative soft decision decoding of various codewords to seek the highest possible coding gain. In current and next-generation optical communications, very powerful FEC codes are crucial for enhancing the transmission distance and rate. Compared with other codewords such as Turbo, LDPC (low density parity check) codes based on sparse matrices have the advantages of being able to perform parallel iterative decoding, having a large throughput, being easy to implement in hardware, having a high codeword flexibility, having variable code lengths and code rates, and having a low bit error rate floor, and are very suitable for high-speed optical communication systems. LDPC codes are the simulation results closest to the channel capacity in an additive white Gaussian noise (AWGN) channel. It is currently the coding scheme for IEEE802.3n, IEEE802.16e, 5G, 40G, 100G to 400G long-distance optical fiber transmission, next-generation Ethernet passive optical network (NG-EPON), etc.

[0003] In terms of LDPC code decoding in optical fiber communication systems, the most traditional bit flipping (BF) algorithm is a hard-decision-based LDPC code decoding algorithm. Subsequently, in order to improve the decoding performance of the BF algorithm, algorithms such as weighted bit flipping (WBF) that introduces different reliability metric values to different parity-check equations and gradient bit flipping (GBF) that utilizes log-likelihood ratio (LLR) information have been proposed. Although these algorithms have low complexity, their decoding performance is relatively low. The sum-product algorithm (SPA) is a soft-information-based decoding algorithm. Its bit error rate performance is only 0.0045 dB away from the Shannon limit, but its complexity is very high, and implementing it requires too much hardware resources. Therefore, the min-sum algorithm (MSA) simplifies the SPA. However, compared with the SPA, the approximation of the MSA will cause a considerable performance loss. The normalized min-sum algorithm (NMS), offset min-sum (OMS) algorithm, and normalized offset min-sum algorithm (NOMS) introduce a normalization coefficient, an offset coefficient, and both a normalization coefficient and an offset coefficient on the basis of the MSA, improving the bit error rate of the MSA. When the parameter values are appropriate, they can approximate the SPA. Among them, in the AWGN channel, through density evolution (DE) analysis, the normalization coefficient and the offset coefficient are respectively recommended to be 0.8 and 0.15. In an optical fiber communication link, there may be various non-linear effects and inter-symbol interference at the transmitter, the optical fiber, and the receiver, far from the AWGN channel. Therefore, in an optical fiber communication system, there is an urgent need for a method to determine appropriate normalization coefficients and offset coefficients to make LDPC code decoding more accurate. Summary of the Invention

[0004] For LDPC decoding algorithms, learnable normalization / offset factors are added to the NMS / OMS decoder to provide a more hardware-friendly neural decoder. However, for these neural network (NN)-based LDPC code decoding algorithms, the parameters of their NMS, OMS, or NOMS decoders are determined based on only the AWGN channel with Gaussian additive white noise. The present invention proposes a neural NOMS algorithm based on NN for an optical fiber communication link with various non-linear effects, making the performance of LDPC codes better in optical communication.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] For a QC-LDPC (quasi-cyclic LDPC) code (N, K), where N is the codeword length, K is the length of information bits, and M is the length of parity-check bits (M = N - K). Its parity-check matrix is H. The dimension of its corresponding exponent matrix E(H) is (N b , K b ), where N b and N b - K b are the number of columns and rows of E(H), Nb = N / Z, K b = K / Z, M b = M / Z = N b -K b 。I is the number of edges in the Tanner graph, E b is the number of edges in E(H). The H matrix can be represented by a Tanner graph, which consists of N variable nodes v n , M check nodes c m and I edges e i where n ∈ {0, 1,..., N - 1}, m ∈ {0, 1,..., M - 1} and i ∈ {0, 1,..., I - 1}. If the (m, n)-th entry of the parity-check matrix H is 1, then the i-th edge connects the m-th check node and the n-th variable node. The neighbors of variable node v n are check nodes c m , m ∈ A(n), where A(n) is the index set of the check nodes connected to variable node v n . Similarly, the neighbors of check node c m are variable nodes v n , n ∈ B(m), where B(m) is the index set of the variable nodes connected to check node c m . A (N, K) LDPC code is obtained by turning each element in E(H) into a cyclic shift matrix over Z×Z or a all-zero matrix. Thus, this property of QC-LDPC codes allows the neural-network-based NOMS decoder to apply the same parameters to all edges of the same edge type.

[0007] The input layer of the neural network takes as input a vector of size N, which is the codeword length; the input to the neural network is the N bits received over the channel; the output is the estimated N transmitted bits, and the structure of the neural network is constructed according to the parity-check matrix H. All subsequent layers in the network, except the last layer (i.e., all hidden layers), are of size I. The hidden layer index corresponding to the d-th iteration in the NOMS decoding process is also d (d = 1, 2,..., d max ). Each hidden layer consists of two sub-layers d v and d c , corresponding to variable-node update and check-node update respectively. The output layer contains N neurons. Its basic structure Figure 1 is shown. For an edge e(v n , c m ) in hidden layer d, the neurons in sub-layer d v output messages along the edge from the associated variable node v n to the check node c m . For sub-layer d cThe neurons in m send messages along the edges from the associated check node c n to the variable node v n . The neurons in the first hidden layer corresponding to the edge e(v m ,c n ) are connected to the v n -th element in the input layer. The neurons in the hidden layer d (d > 1) corresponding to the edge e(v m ,c are connected to the neurons in the sub-layer of the hidden layer d - 1 associated with the edge and c m' ≠c m . The neurons in the sub-layer d of the hidden layer d (d ≥ 1) corresponding to the edge e(v ,c n ) are connected to the neurons in the sub-layer d m associated with the edge e(v c ,c v ) and v n ≠v m' . The edge e(v n' ,c n ) is the edge connecting the n-th variable node v n , check node c m' in the Tanner graph, and c n is the check node in the set A(n). m' m' Specifically, the steps include:

[0008] 1. For QC-LDPC codes, each hidden layer of the neural network NN includes two sub-layers, which are used to update variable nodes and check nodes respectively; all I neurons in each sub-layer can be divided into Z groups, and each group contains E b elements, which correspond to the number of edges on the exponent matrix. Therefore, I = ZE b .

[0009] 2. Consider the d-th hidden layer,

[0010] is the neuron in sub-layer d v processing e(v n ,c m ). The output message of this neuron can be expressed as: where, is the log-likelihood ratio of the channel, which is related to the received information r n in the optical fiber communication link, and r n ​​For the N bits received by the receiver of an optical fiber communication system, there is an additive white Gaussian noise channel with an average value of 0 and a variance of σ in the communication channel of the optical fiber communication link. A(n)\m is the index set of the check node A(n) excluding c m For all e(v n ,c m' ), its initialization

[0011] 3. is the neuron that processes e(v c in sub-layer d n ,c m ). The output information of the neuron can be expressed as: where B(m)\n is the index set of the variable node B(m) excluding v n . e(v n ,c m' ) is the edge connecting the nth variable node v n and the check node c m' in the Tanner graph. c m' is the check node in the set A(n) excluding c m . B(m) is the index set of the variable nodes connected to the check node c m . e(v n ,c m' ) is the edge connecting the variable node v n' and the check node c m in the Tanner graph. v n' is the variable node in B(m) excluding v n . is the normalization coefficient of the edge e(v n ,c m ) in the dth iteration. is the bias coefficient of the edge e(v n ,c m ) in the dth iteration.

[0012] 4. The information output by the output neuron is: where the activation function sigmoid() ensures that the output value of the final neural network is between 0 and 1. Therefore, o n is the probability that the transmitted bit w n = 0. During the training process, the weights and biases in the neuron change with the number of decoding iterations d (d = 1, 2,..., d max ). The maximum number of decoding iterations d max is equal to the total number of hidden layers of the neural network.

[0013] 5. Use the cross - entropy between the codeword w transmitted in the actual optical fiber communication link and the output o of the neural - network - based NOMS decoder as the loss function, which is defined as: where w n and o n are the nth transmitted codeword and the neural - network output respectively. To find the optimal normalization factor and offset factor, the training method is to construct the NOMS decoding neural network according to the structure, and adjust the weights and biases for all d max iterations to minimize the loss function. During the online process, the fixed and are directly used for iterative update.

[0014] Compared with the prior art, the positive effects of the present invention are:

[0015] The present invention improves the performance of the LDPC code decoding algorithm by the NN learning the characteristics of the optical communication channel, enabling the LDPC code to be fully utilized in the optical transmission system. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is a schematic structural diagram of the NN - NOMS decoder.

[0017] Figure 2 is a simulation block diagram of a short - distance optical interconnection system based on VPI.

[0018] Figure 3 is the bit - error rate performance of codeword 1.

[0019] Figure 4 is the α value of E b neurons of codeword 1.

[0020] Figure 5 is the β value of E b neurons of codeword 1.

[0021] Figure 6 is the bit - error rate performance of codeword 1 with the number of iterations when ROP = 4dBm.

[0022] Figure 7 is the bit - error rate performance of codeword 1 in the scenario of 100Gb / s and 100m.

[0023] Figure 8 is the bit - error rate performance of codeword 1 in the scenario of 100Gb / s and btb.

[0024] Figure 9 is the α value of E b neurons of codeword 2.

[0025] Figure 10 is the β value of E bThe β value of a neuron.

[0026] Figure 11 is the bit error rate performance of codeword 2. Detailed implementation manners

[0027] The present invention will be described in detail below through specific embodiments in conjunction with the accompanying drawings.

[0028] VPItransmissionMaker V10.0 (VPI) is used to establish a simulation platform for short-distance optical interconnection systems within a data center, as Figure 2 shown. The vertical cavity surface emitting lasers (VCSELs), multimode fibers (MMFs), and photodetectors in the simulation platform introduced in this section all use the modules provided by VPI. Since it has been proven that neural networks can estimate the transmission law of a part of the pseudo-random code (PRBS), thus overestimating the performance, therefore, at the transmitting end, we generate Gaussian distribution random numbers with a mean of 0 and a variance of 1, and then judge their signs to determine the transmitted bits and generate non-return-to-zero (NRZ) signals. The optical carrier is generated by an 850 nm VCSEL with a 3 dB bandwidth of approximately 3 GHz. Then, optical signals are transmitted at a rate of 100 Gb / s in an MMF with a length of 100 m and in an end-to-end (btb) scenario. The receiver uses a variable optical attenuator (VOA) to adjust the received optical power. After the optical signal is detected by a photodiode (PD), forward equalization (FFE) and LDPC code decoding are performed in sequence to obtain the recovered bits and calculate the bit error rate.

[0029] The base code used in the simulation is the BG1 matrix in the 5G standard, and its parity check matrix H BG1 has 46 rows and 68 columns. The code rate of test codeword 1 (2240, 1760) is 5 / 6, Z = 80, and its E b = 87. The code rate of test codeword 2 (2232, 1584) is 3 / 4, Z = 72, and its E b = 113. Train LDPC codes with a length of 1000 frames and test LDPC codes with a length of 1000 frames. After determining the values of α and β, the number of NOMS iterations is 25 times. The bit error rate performance of codeword 1 in a 100 m optical interconnection link at 100 Gb / s is as Figure 3 shown. At BER = 10 -3 , the neural network-based NOMS algorithm, that is, the NN-NOMS algorithm, can bring a gain of nearly 4 dB compared with the traditional NOMS algorithm.

[0030] Figure 4 and Figure 5 are when the rate is 100 Gb / s, the transmission distance is 100 m, and ROP = 4 dBm, and the E of test codeword 1 bThe normalized value α and bias value β of a neuron. It can be seen that the α values are concentrated around 0.895 and the β values are concentrated around 0.053. Therefore, we tried to fix the α value at 0.89 and the β value at around 0.05. When the received signal-to-noise ratio (ROP) = 4 dBm, the bit error rate performance of the obtained test codeword 1 with the number of iterations is as Figure 6 shown (NN-NOMS-Fix is the curve after fixing the values). It can be seen that after the parameter values are fixed, the performance of the NN-NOMS-Fix algorithm and the NN-NOMS algorithm is almost the same.

[0031] Figure 7 and Figure 8 are the bit error rate performances of the NN-NOMS-Fix algorithm, NN-NOMS, and NOMS of test codeword 1 when the transmission distances are 100 m and btb respectively in the scenario of 100 Gb / s. At this time, for different ROPs, we used the fixed α value and β value obtained by training at any one power point. The bit error rate performances of the NN-NOMS-Fix algorithm and the NN-NOMS algorithm are similar and significantly better than the traditional NOMS algorithm. Therefore, our method can not only well learn various nonlinear effects of the optical fiber communication system, but also has strong generalization ability. For the same LDPC code of the same channel, we only need to train once to obtain appropriate parameter values. After that, for transmission links with different received optical powers, there is no need to retrain.

[0032] Figure 9 and Figure 10 are the α and β values of E b neurons of test codeword 2 when the rate is 100 Gb / s, the transmission distance is 100 m, and NN-NOMS is trained four times at ROP = 0 dBm. It can be seen that the α values are concentrated around 0.893 and the β values are concentrated around 0.06. Therefore, in the NN-NOMS-Fix algorithm, we tried to fix the α value at 0.89 and the β value at around 0.06.

[0033] Figure 11 are the bit error rate performances of test codeword 2 when the rate is 100 Gb / s and the transmission distances are 100 m and btb. When the BER = 10 -5 or so, compared with the traditional NOMS algorithm, the NN-NOMS algorithm can bring about 2 dB and 1 dB signal-to-noise ratio gains respectively. The bit error rate performances of the NN-NOMS-Fix algorithm and the NN-NOMS algorithm are similar, further proving that the NN-NOMS algorithm has strong generalization ability.

[0034] Although specific embodiments of the present invention are disclosed for illustrative purposes, which are intended to help understand the content of the present invention and implement it accordingly, those skilled in the art can understand that various substitutions, changes, and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the present invention should not be limited to the content disclosed in the best embodiments, and the scope of protection claimed by the present invention shall be defined by the scope defined in the claims.

Claims

1. A decoding method of LDPC codes based on neural network in an optical fiber communication system, the steps of which include: 1) Construct a neural network according to the quasi-cyclic LDPC code to be decoded; wherein, the neural network includes an input layer, a plurality of hidden layers, and an output layer connected in sequence, and each of the hidden layers includes a sub-layer for updating variable nodes and a sub-layer for updating check nodes; all I neurons of each sub-layer are divided into Z groups, and each group contains E b neurons, and I = ZE b ; N is the codeword length of the quasi-cyclic LDPC code, and K is the information bit length of the quasi-cyclic LDPC code; the check bit length M of the quasi-cyclic LDPC code is M = N - K, the check matrix is H, and the dimension of the exponent matrix E(H) of the check matrix H is (N b , K b ), N b is the number of columns of E(H), and N b - K b is the number of rows of E(H); the check matrix H is represented by a Tanner graph, which is composed of N variable nodes, M check nodes, and I edges, and e(v n , c m ) is the edge connecting the nth variable node v n , the mth check node c m in the Tanner graph; 2) The input layer generates a vector of length N based on the input quasi-cyclic LDPC and inputs it into the first hidden layer; the d-th hidden layer includes sub-layer d for updating variable nodes v and sub-layer d for updating check nodes c , and the neurons in sub-layer d v are used to output messages along the edge sent from the associated variable node v n to the check node c m . There are a total of I neurons, and the neurons in sub-layer d c are used to output messages along the edge sent from the associated check node c m to the variable node v n . There are a total of I neurons; the output message of the neuron representing the edge e(v v , c n ) in sub-layer d m is = is the channel log-likelihood ratio for transmitting the quasi-cyclic LDPC code, A(n)\m is the index set of the check node A(n) excluding c m , e(v n , c m' ) is the edge connecting the n-th variable node v n , check node c m' in the Tanner graph, c m' is the check node in the set A(n) excluding c m , initialization sub-layer d c the output message of the neuron representing the edge e(v n , c m ) B(m)\n is the index set of the variable node B(m) excluding v n , B(m) is the index set of the variable nodes connected to the check node c m , e(v n , c m' ) is the edge connecting the variable node v n' , check node c m in the Tanner graph, v n' is the variable node in B(m) excluding v n , is the normalization coefficient of the edge e(v n , c m ) in the d-th iteration, is the bias coefficient of the edge e(v n , c m ) in the d-th iteration; where d = 1, 2,..., d max , d max The total number of hidden layers of the neural network; 3) The output layer obtains the decoded result based on the output of the last hidden layer wherein is the output information at the last iteration.

2. The method according to claim 1, wherein The loss function for training the neural network is as follows: where w n is the nth quasi-cyclic LDPC code transmitted by the communication system, and o n is the decoding output by the neural network based on the input codeword w n , and N is the total number of quasi-cyclic LDPC codes used for training.

3. The method according to claim 1, characterized in that, The neuron corresponding to edge e(v n , c m ) in the first hidden layer is connected to the v n -th element in the input layer. The neuron corresponding to edge e(v n , c m ) in the d-th hidden layer is connected to the neurons in sub-layer (d - 1) n , c m' ) of the (d - 1)-th hidden layer that is associated with edge e(v m' ≠ c m . The neuron corresponding to edge e(v c , c c ) in sub-layer d n , c m ) is connected to the neurons in sub-layer d v that are associated with edge e(v n , c m' ) and v n' ≠ v n .

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