CN112564716B - PC-SCMA system joint decoding method based on pruning iteration - Google Patents

Abstract

The present invention provides a PC-SCMA system joint decoding method based on pruning iteration, said method comprising: Step 1: performing CRC encoding before polar encoding and SCMA encoding; Step 2: undergoing polar encoding and SCMA encoding After the codeword of the resource node is transmitted through the channel, the confidence stability value of each branch of the resource node is calculated; Step 3: The obtained confidence stability value is first propagated to the branch with a large stability deviation in adjacent iterations, And dynamically reduce the factor graph that participates in the next iteration; Step 4: Perform SCMA and SCAN joint iterative detection and decoding according to the dynamic factor graph; Step 5: Perform CRC check on the decoded codeword, if the check is passed, Terminate the iteration, if not passed, return to step 2. The invention solves the problems of high calculation complexity, slow convergence speed and high bit error rate of the joint decoding algorithm of SCMA and polar code.

Description

A joint decoding method for PC-SCMA system based on pruning iteration

technical field

The invention relates to the technical field of wireless communication, in particular to a PC-SCMA system joint decoding method based on pruning iteration.

Background technique

Polar code (Polar Code, PC) is a kind of channel coding theory that has been strictly proved to be able to reach Shannon tolerance under binary-discrete memory less channel (B-DMC). As a control channel standard coding scheme supporting enhanced mobile broadband, polar codes have excellent error correction performance, and their coding and decoding complexity is lower than Turbo codes and LDPC (low density parity check) codes.

Sparse Code Multiple Access SCMA (Sparse Code Multiple Access) technology combines high-dimensional modulation and sparse spread spectrum to directly map bit data streams into complex-domain multi-dimensional codewords in a preset codebook for Solve the system overload situation of massive connections. On the detection side, due to the sparsity of the SCMA codebook, the traditional maximum a posterior probability (MAP) detection can be replaced by a message passing algorithm (MPA) to obtain approximate bit errors with lower complexity. performance.

In practical applications, SCMA needs to be combined with channel coding techniques to obtain better quality of service (QOS), and these channel coding techniques include Turbo codes, LDPC codes, and polar codes. For the scheme of separate detection and decoding at the receiving end, the ideal bit error performance cannot be achieved due to the inability to make full use of the intermediate information, and the computational complexity is relatively high.

Contents of the invention

The purpose of the present invention is to solve the problem of high total power consumption of the existing SCMA network system and waste of system resources according to channel gain. The present invention provides a PC-SCMA system joint decoding method based on pruning iteration.

In order to achieve the purpose and advantages according to the present invention, a PC-SCMA system joint decoding method based on pruning iteration is provided, the data stream is interleaved with codewords after polar encoding, and then encoded by SCMA, the method includes Follow the steps below:

Step 1: CRC encoding is performed before polar encoding and SCMA encoding;

Step 2: Calculate the confidence stability value of each branch of the resource node after the polarized coded and SCMA coded codewords are transmitted through the channel;

Step 3: Propagate the obtained confidence stability value preferentially to branches with larger stability deviations in adjacent iterations, and dynamically reduce the factor graph participating in the next iteration;

Step 4: Perform SCMA and SCAN joint iterative detection and decoding according to the dynamic factor graph;

Step 5: Perform CRC check on the decoded codeword, if the check is passed, terminate the iteration, if not, return to step 2.

Preferably, in the first step, the CRC-encoded codeword is placed at the end of the polar-encoded codeword.

Preferably, the method for calculating the confidence stability value of each branch of the resource node in the step 2 includes:

Step 21: Sequential resource node message update, for the tth iteration, the message update of resource node k is expressed as:

In the formula, r _K represents resource block k, u _j represents user j, x _j represents the code word of user j after SCMA encoding, y _k represents the received signal on resource block k, h _kv represents the distance between resource k and user v Channel gain, ε _k is the non-zero position set of the kth row of the factor matrix updated after t-1 iterations, ε _k /{i,j} means excluding elements i and j from the set ε _k , and i≠j, i∈ε _k , j∈ε _k . σ ² is the noise variance, [] ^old and [] ^new represent the message before and after the resource node updates the codeword message;

Step 22: Calculate the confidence stability value of each branch according to the updated resource node message, and use it for the next iteration. In the tth iteration, the confidence stability of the message from resource node k to user node j is

Among them, χ _j represents the set of codewords encoded by SCMA.

最大的分枝，使其不再参与下一次资源节点的消息更新。Preferably, the method for dynamically reducing the factor graph participating in the next iteration in the step 3 is: in the next iteration, the factor graph will be removed from the factor graph

The largest branch makes it no longer participate in the next message update of resource nodes.

Preferably, when the information of the resource node is updated for the first time, the original factor graph is used for updating.

Preferably, the step of joint iterative detection and decoding in step 4 includes:

Step 41: Obtain the symbol message according to the updated message of the resource node, and then map the symbol message into a bit message, and convert it into the form of log likelihood ratio;

表示为：The symbol message obtained according to the updated message of the resource node

Expressed as:

为用户j的第l个发送信号，ζ_j表示因子矩阵第j列的非零位置集，t_max表示最大迭代次数，将符号消息映射为比特消息由以下公式计算：In the formula,

is the lth transmission signal of user j, ζ _j represents the non-zero position set of the jth column of the factor matrix, t _max represents the maximum number of iterations, and the symbol message is mapped to the bit message by the following formula:

表示满足映射关系：In the formula, Q=log ₂ M, where M is the SCMA codeword dimension, b _{j, (l-1)Q+m} represents the [(l-1)Q+m]th bit message of user j,

Indicates that the mapping relationship is satisfied:

的码字集合，

同理可得到；将比特消息转化为对数似然比消息形式可由以下公式计算：

set of codewords,

In the same way, it can be obtained; converting the bit message into the log likelihood ratio message form can be calculated by the following formula:

Then, the log-likelihood ratio after message deinterleaving can be expressed as:

Among them, П ^-1 represents the deinterleaving operation;

右消息

初始化为：Step 42: Deinterleave the log-likelihood ratio message and input it into the polar decoder and use the SCAN algorithm for decoding, and initialize the left message and the right message of the factor graph of the SCAN algorithm; the left message is initialized as polar decoding prior information

right message

Initialized as:

Wherein, n=log ₂ (N), N is the code length of the polar code, I represents the message bit set, and I ^C represents the frozen bit set;

Step 43: The initialized left message and right message are transmitted and updated in the SCAN factor graph, which can be calculated by the following formula:

where L _s,t , R _s,t denote the left message and right message of user j respectively, where s, t denote the row and column index respectively, and f(a,b)≈sign(a)×sign(b) ×min(|a|,|b|);

Step 44: After the left message and the right message arrive at the leftmost end and the rightmost end of the SCAN factor diagram respectively, they are interleaved, and then input to the SCMA decoder as a priori message and expressed as:

和

分别表示

和

的均值；当SCMA译码器接收到的先验消息后，首先转化为概率消息由下式计算：Where c _j,(l-1)Q+m represents the (l-1)Q+m codeword of user j, П represents the interleaving operation, and a is the weight factor

with

Respectively

with

The mean value of ; when the SCMA decoder receives the prior message, it is first converted into a probability message and calculated by the following formula:

Among them, q _j,m ∈ {0, 1}; then the probability message is mapped to the symbol message of the SCMA decoder, expressed as:

Preferably, the value of the weight factor a in the step 4 or 4 depends on the code rate. When the code length N=256 and the code rate R=0.47, the value of the weight factor a is 0.6; when the code length N=1024, When the code rate R=0.32, the value of the weight factor a is 0.4.

Preferably, the checking method in the fifth step is to judge the output message of joint detection and decoding, and perform CRC check on the judgment result.

Preferably, the verification method is to perform verification in each iteration process, and if the verification is not passed, the next iteration is performed and terminated after the maximum number of iterations is reached.

The above technical features can be combined in various suitable ways or replaced by equivalent technical features, as long as the purpose of the present invention can be achieved.

The beneficial effect of the present invention is that, aiming at the high complexity of the PC-SCMA system joint detection decoding algorithm and unsatisfactory bit error performance, a pruning iterative decoding algorithm based on the stability of the confidence degree of the resource node is firstly proposed, and the dynamic adjustment needs to be carried out Branching of message updates to avoid redundant iterations can reduce computational complexity by 24% to 50%. Secondly, a cyclic redundancy check termination mechanism is added in the joint iteration process to avoid decoding deviation caused by too small signal-to-noise ratio. The simulation results show that, compared with the existing joint decoding scheme, the proposed decoding scheme The bit error rate performance has been significantly improved. Finally, the joint algorithm of the two schemes can achieve good bit error performance while reducing the computational complexity.

Description of drawings

FIG. 1 is a model diagram of a polar code SCMA system with a CRC termination mechanism added in the present invention.

Fig. 2 is a model diagram of the uplink polar code SCMA communication system of the present invention.

Fig. 3 is a schematic diagram of the traditional message delivery process of the present invention.

FIG. 4 is a schematic diagram of the message passing process based on pruning iteration of the present invention.

Fig. 5 is a diagram of decoding factors of polar code SCAN.

Fig. 6 is a schematic diagram of unit factor graph message passing.

Figure 7 is a flowchart of the PIC-JDD algorithm.

Figure 8 is a histogram comparing the operational complexity of different algorithms.

FIG. 9 is a simulation diagram of PI-JDD BER performance comparison when N=256.

Fig. 10 is a simulation diagram of PI-JDD BER performance comparison when N=1024.

Fig. 11 is a simulation diagram of C-JIDD BER performance comparison when N=256.

Fig. 12 is a simulation diagram of C-JIDD BER performance comparison when N=1024.

Fig. 13 is a simulation diagram of PIC-JDD BER performance comparison when N=256.

Fig. 14 is a simulation diagram of PIC-JDD BER performance comparison when N=1024.

detailed description

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

It should be noted that, in the case of no conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

With reference to Fig. 1 adding redundancy check (cyclic redundancy check, CRC) as shown in the polar code SCMA system model diagram of termination mechanism, the realization steps of the present invention are as follows:

Step 1: CRC encoding is performed before polar encoding and SCMA encoding.

In each joint iteration, some codewords reach the correct codeword during the decoding process, but as the number of iterations increases, they will deviate from the correct codeword, so that even if the maximum number of iterations is reached, it will eventually converge to the wrong codeword. Therefore, a cyclic redundancy check is added in each joint iteration process, and the codeword is locked in time when the correct codeword is decoded, and the decoding iteration is terminated.

The cyclic redundancy check requires adding a CRC code during the encoding process, so a small part of the code rate needs to be sacrificed, but good detection performance can be achieved. The CRC code is added after the polar code word, and the message bits and the CRC check code word are mapped together into free bits of the polar code for transmission. At the receiving end, CRC checks whether the decoded codeword is a valid codeword in each iteration, and if the judgment is correct, the codeword is returned and the iteration is terminated.

Step 2: Calculate the confidence stability value of each branch of the resource node after the polarized coded and SCMA coded codewords are transmitted through the channel.

The data stream is interleaved with polar coded codewords, and then SCMA coded, as shown in Figure 2, this embodiment is aimed at an uplink SCMA and polar code combined system, the information bits of J users U={u ₁ , u ₂ ,…,u _J }, where u _j ＝{u _j,1 ,u _j,2 ,…,u _j,m }, after polarization coding, it becomes C={c ₁ ,c ₂ ,…,c _J }, where c _j ={c _j,1 ,c _j,2 ,...,c _j,N }, 1≤j≤J. After polar encoding, the codeword of each user is {b ₁ , b ₂ ,...,b _J } after interleaving. After b _j is encoded by SCMA, it is mapped to an M-dimensional complex code word x _j ={x _j,1 ,x _j,2 ...,x _j,M }, and the mapping function of SCMA encoding is defined as g _j :{b _j,1 , b _j,2 ,...,b _j,Q }→{x _j,1 ,x _j,2 ...,x _j,M }, Q=log ₂ M, x _j,m ∈C. J users share K orthogonal time-frequency resources (J>K) and transmit to the same base station.

Since the SCMA codeword is M-dimensional, and each codeword is composed of J user symbols, the overload rate of the SCMA system is J/M. The factor matrix containing 6 user nodes and 4 resource nodes is expressed as follows:

For an uplink SCMA system, the channel gain matrix between the base station and the jth user is expressed as:

表示资源k与用户j之间的信道增益。在接收端，第l个接受信号表示为：in,

Indicates the channel gain between resource k and user j. At the receiving end, the l-th accepted signal is expressed as:

表示用户j的第l个SCMA码字。

为高斯白噪声且z^l～CN(0，δ²I)。where 1≤l≤L=N/Q,

Indicates the lth SCMA codeword of user j.

It is Gaussian white noise and z ^l ～CN(0, δ ² I).

In the traditional joint iterative detection and decoding scheme, each resource node (resource nodes, RNs) sequentially transmits messages to all connected user nodes (user nodes, UNs) during each round of iteration, as shown in Figure 3. But in the actual update process, the convergence speed of different branches in the factor graph is different. At the same time, not all messages are equally useful for convergence. In addition, the complexity of the MPA algorithm is mainly reflected in the update of resource nodes. Therefore, after each round of iteration, the converged branches are eliminated according to the confidence stability value of the resource node, and the system factor graph is dynamically adjusted, which can effectively reduce the computational complexity. Secondly, adding a cyclic redundancy check termination mechanism in the iterative process can avoid decoding deviation caused by too small signal-to-noise ratio, and exit the iteration early, which can significantly improve the bit error performance.

Preferably, the method for calculating the confidence stability value of each branch of the resource node in the step 2 includes:

Step 21: Sequential resource node message update, for the tth iteration, the message update of resource node k is expressed as:

In the formula, r _K represents resource block k, u _j represents user j, x _j represents the code word of user j after SCMA encoding, y _k represents the received signal on resource block k, h _kv represents the distance between resource k and user v Channel gain, ε _k is the non-zero position set of the kth row of the factor matrix updated after t-1 iterations, ε _k /{i,j} means excluding elements i and j from the set ε _k , and i≠j, i∈ε _k , j∈ε _k . σ ² is noise variance. [] ^old and [] ^new represent the messages before and after the resource node updates the codeword message.

Step 22: Calculate the confidence stability value of each branch according to the updated resource node message, and use it for the next iteration. In the tth iteration, the confidence stability of the message from resource node k to user node j is

最大的分枝为最接近收敛分枝，表明此分枝在本次迭代中并未产生有效的更新消息，在下次迭代中将其从因子图中剔除，如图4中虚线所示。Among them, χ _j represents the set of codewords encoded by SCMA.

The largest branch is the closest to the convergent branch, indicating that this branch does not generate effective update messages in this iteration, and it will be removed from the factor graph in the next iteration, as shown by the dotted line in Figure 4.

Step 3: The obtained confidence stability value is first propagated to the branch with a large stability deviation in adjacent iterations, and the factor graph participating in the next iteration is dynamically reduced.

最大的分枝，使其不再参与下一次资源节点的消息更新。优选的是，所述资源节点的消息更新为首次更新时，由于无法区分分枝收敛快慢，因此采用原始因子图进行更新。Preferably, the method for dynamically reducing the factor graph participating in the next iteration in the step 3 is: in the next iteration, the factor graph will be removed from the factor graph

The largest branch makes it no longer participate in the next message update of resource nodes. Preferably, when the information of the resource node is updated for the first time, the original factor graph is used for updating because it is impossible to distinguish the speed of branch convergence.

Step 4: Perform SCMA and soft cancellation (soft cancellation, SCAN) joint iterative detection and decoding according to the dynamic factor graph.

After deinterleaving, the user messages calculated by all resource nodes are mapped to prior messages decoded by polar codes for SCAN decoding. The message decoded by the polar code is used as prior information to update the resource node message. The message passing process is shown in Figure 4.

Preferably, the step of joint iterative detection and decoding in step 4 includes:

Step 41: Obtain the symbol message according to the updated message of the resource node, and then map the symbol message into a bit message, and convert it into the form of log likelihood ratio.

表示为：The symbol message obtained according to the updated message of the resource node

Expressed as:

为用户j的第l个发送信号，ζ_j表示因子矩阵第j列的非零位置集，t_max表示最大迭代次数。将符号消息映射为比特消息由以下公式计算：In the formula,

is the l-th transmission signal of user j, ζ _j represents the non-zero position set of column j of the factor matrix, and t _max represents the maximum number of iterations. The mapping of symbolic messages to bit messages is calculated by the following formula:

表示满足映射关系：

的码字集合，

同理可得到；将比特消息转化为对数似然比消息形式可由以下公式计算：In the formula, Q=log ₂ M, where M is the SCMA codeword dimension, b _{j, (l-1)Q+m} represents the [(l-1)Q+m]th bit message of user j,

Indicates that the mapping relationship is satisfied:

set of codewords,

In the same way, it can be obtained; converting the bit message into the log likelihood ratio message form can be calculated by the following formula:

Then, the log-likelihood ratio after message deinterleaving can be expressed as:

Among them, П ^-1 represents the deinterleaving operation.

As an implementation, the polar code factor diagram of code length N=8 is as shown in Figure 5, which consists of log ₂ (N)+1=4 columns, and the unit factor diagram of each adjacent column is shown in Figure 6, L _s,t , R _s,t represent the left message and the right message respectively, where s, t represent the row and column index respectively. Each point in the polar coding factor graph can be represented by a (λ, β, φ). where λ represents the layer of the factor graph. β is represented as the serial number of the box (group), and the number of boxes contained in the λth layer is 2 ^n-λ , n=log ₂ (N). φ is expressed as the serial number of the point in the box. As shown in Fig. 5, there are four points in the box labeled β=0 and 1 in the λ=2 layer box, which are marked as φ=1, 2, 3, 4 respectively. Obviously, for the λ layer, there are 2 ^λ points in each box. For user j, the message delivery process is as follows.

右消息

初始化为：Step 42: Deinterleave the log-likelihood ratio message and input it into the polar decoder and use the SCAN algorithm for decoding, and initialize the left message and the right message of the factor graph of the SCAN algorithm; the left message is initialized as polar decoding prior information

right message

Initialized as:

Wherein, n=log ₂ (N), N is the code length of the polar code, I represents the message bit set, and ^IC represents the frozen bit set.

Step 43: The initialized left message and right message are transmitted and updated in the SCAN factor graph, which can be calculated by the following formula:

where L _s,t and R _s,t denote the left message and right message of user j respectively, where s, t denote the row and column index respectively, and f(a,b)≈sign(a)×sign(b) ×min(|a|,|b|).

Step 44: After the left message and the right message arrive at the leftmost end and the rightmost end of the SCAN factor diagram respectively, they are interleaved, and then input to the SCMA decoder as a priori message and expressed as:

和

分别表示

和

的均值；当SCMA译码器接收到的先验消息后，首先转化为概率消息由下式计算：Where c _j,(l-1)Q+m represents the (l-1)Q+m codeword of user j, П represents the interleaving operation, and a is the weight factor

with

Respectively

with

The mean value of ; when the SCMA decoder receives the prior message, it is first converted into a probability message and calculated by the following formula:

Among them, q _j,m ∈ {0, 1}; then the probability message is mapped to the symbol message of the SCMA decoder, expressed as:

Preferably, the value of the weight factor a in the step 4 or 4 depends on the code rate. When the code length N=256 and the code rate R=0.47, the value of the weight factor a is 0.6; when the code length N=1024, When the code rate R=0.32, the value of the weight factor a is 0.4.

Step 5: Perform a CRC check on the decoded codeword. If the check is passed, the iteration is terminated. If the check is not passed, return to step 2. Preferably, the next iteration is performed, and the iteration is terminated after reaching the maximum number of iterations. Preferably, the verification method is to judge the output message of the joint detection and decoding, and perform CRC verification on the judgment result.

The complexity of the PC-SCMA system joint detection and decoding algorithm is mainly reflected in the update process of resource nodes and the code length of polar codes. Compared with joint detection and decoding (JDD) and joint iterative detection and decoding (JIDD) algorithms, the algorithm of the present invention removes the branch with the highest stability so that it no longer Update resource nodes and dynamically reduce the factor graph participating in iterations to reduce computational complexity. Table 1 describes the complexity of the addition, multiplication and comparison operations of the two algorithms, where T represents the maximum number of iterations, and d _f is the number of users occupied by each resource block.

Table 1 Computational complexity of different algorithms

FIG. 7 is an algorithm flow chart of the pruning iterative joint detection and decoding (PIC-JDD) algorithm adding CRC check in the present invention. The comparison results of the complexity of the PIC-JDD algorithm proposed by the present invention and the traditional JIDD algorithm when the code lengths are 256 and 1024 and T=7 are shown in FIG. 8 . It can be seen that the PIC-JDD algorithm has a significant reduction in both addition and multiplication operations than JIDD. When PIC-JDD and JIDD were at code length N=256, the number of adders was 20796 and 41972 respectively, and when code length N=1024, the number of multipliers was respectively 66048 and 87808, and the algorithm of the present invention saved about 50% of the number of adders and 24% multiplier. In addition, compared with the JIDD algorithm, the present invention adds a comparison operation in the pruning process, and the number of operations is 72 under the two code lengths. In the update process of the resource node, the algorithm of the present invention removes the stable branches in the previous two iterations from the next iteration, avoids redundant updates, and effectively reduces the computational complexity.

With the help of Matlab software, the joint detection and decoding scheme proposed in this embodiment is compared and simulated with the traditional joint detection and decoding algorithm to evaluate its performance. Secondly, under the same conditions, the system performance under different code lengths is analyzed. The following simulation is the performance comparison curve obtained when the code length is 256 and 1024 respectively under the Gaussian channel. When N=256, the system code rate R=1/2, and the weight factor a=0.6; when N=1024, the system code rate R= 1/3, weight factor a=0.4. The parameter settings are shown in Table 2:

Table 2 Simulation parameters

Performance analysis of the joint detection decoding scheme (PI-JDD) based on pruning iteration: the BER performance curves of the code length N=256 and N=1024 when the number of iterations are 5 and 7 respectively are shown in Figure 9 and Figure 10. It can be seen from Fig. 9 that when the code length is 256 and the signal-to-noise ratio (1-3dB) is small, the BER performance curve of the PI-JDD algorithm almost completely coincides with the traditional JIDD algorithm. With the increase of SNR, the BER performance loss of PI-JDD and JIDD algorithms is less than 5.01×10 ^-4 , because the interference between users increases with the increase of signal power. In addition, it can be seen from Figure 10 that the PI-JDD performance has a slight loss when N=1024 iterates 5 times and 7 times. This is because not all branches participate in each update process during the iteration process, which effectively avoids Redundant iterations. Combining with Fig. 8 and its conclusion, the PI-JDD algorithm proposed in the present invention can effectively reduce the computational complexity under the condition of slight loss of bit error performance.

Performance analysis of the joint detection decoding algorithm (C-JIDD) with the early termination mechanism CRC added: when the code length N=256, the performance comparison between C-JIDD and JIDD BER is shown in Figure 11. It can be seen from the figure that under the same number of iterations, the BER performance of the present invention is better than that of the original JIDD algorithm, because the addition of an early termination mechanism can overcome the decoding caused by convergence errors by locking the correct codeword in advance Deviate. When EbN0=4, the BER of the original JIDD algorithm for 5 iterations=8.45×10 ^-3 , while the BER of the present invention is 7.68×10 ^-4 for 5 iterations, the performance is nearly an order of magnitude better. When EbN0 is less than 3.5, the performance of 3 iterations of the present invention is equivalent to the performance of the original 5 iterations, because adding a CRC termination mechanism can effectively reduce the number of decoding deviations caused by too small signal-to-noise ratio. As the signal-to-noise ratio increases, this gap will gradually decrease. It can also be seen from the figure that when BER=1.53×10 ^-3 , the present invention has a gain of 0.54 dB relative to the original JIDD of 5 iterations.

The performance comparison of C-JIDD and JIDD BER when the code length N=1024 is shown in Figure 12. It can be seen from the figure that under the same number of iterations, the BER performance of the present invention is better than that of the original JIDD algorithm. When EbN0=3, the BER of the JIDD algorithm for 3 iterations=1.74×10 ^-3 , while the BER of the present invention is 4.01×10 ^-4 for 3 iterations. When EbN0 is less than 2.2, the performance of the present invention for 3 iterations is better than that of the traditional 5 iterations. It can also be seen from the figure that when BER=5.98×10 ^-4 , the present invention has a gain of 0.32 dB relative to the original JIDD of 5 iterations.

The performance analysis of the joint detection and decoding optimization scheme (PIC-JDD) based on pruning iteration with CRC checking: the detection and decoding algorithm PIC-JDD simulation after combining the optimization algorithm PI-JDD and C-JIDD proposed by the present invention The results are shown in Figures 13 and 14. The code length N=256, and the BER performance comparison simulation of the PIC-JDD proposed by the present invention and the traditional JIDD algorithm when the number of iterations are 5 and 7 respectively is shown in FIG. 13 . It can be seen from the figure that the BER performance of the PIC-JIDD algorithm proposed by the present invention is better than that of the original JIDD algorithm at two iterations. When EbN0=4.5, 7 iterations of the JIDD algorithm BER=1.1×10 ^-3 , but the present invention has 7 iterations of BER=7.74×10 ^-5 , and the performance is an order of magnitude better. It can also be seen from FIG. 13 that when N=256, the BER performance of the present invention for 5 iterations is better than that of the original JIDD for 7 iterations. At the same time, it can be seen that the performance of the 5 iterations of the present invention is significantly improved compared to the BER performance of the joint detection and decoding of the original MPA and 500 iterations of the BP algorithm [14].

The code length N=1024, when the number of iterations is 5 and 7, the BER performance comparison simulation of the PIC-JDD and JIDD algorithms proposed by the present invention is shown in Figure 14 . It can be seen that the BER performance of the PIC-JDD algorithm proposed by the present invention is better than that of the traditional JIDD algorithm at both iterations. When EbN0=2.6, the traditional JIDD algorithm BER=6.9×10 ^-2 for 5 iterations, and BER=1.9×10 ^-2 for 5 iterations in the present invention. In addition, it can also be seen that when N=1024, the BER performance of 5 iterations of PIC-JDD of the present invention is better than that of 7 iterations of traditional JIDD.

Although the invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It is therefore to be understood that numerous modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the invention as defined by the appended claims. It shall be understood that different dependent claims and features of the present invention may be combined in ways other than those described in the original claims. It will also be appreciated that features described in connection with individual embodiments can be used in other described embodiments.

Claims (7)

1. A joint detection decoding method of a polar code SCMA system based on pruning iteration is characterized in that code words of data streams after being subjected to polar coding are interleaved and then subjected to SCMA coding, and the method comprises the following steps:

the method comprises the following steps: CRC encoding is performed before polarization encoding and SCMA encoding;

step two: after the code words subjected to polarization coding and SCMA coding are transmitted through a channel, the confidence stability value of each branch of the resource node is calculated, and the method for calculating the confidence stability value of each branch of the resource node comprises the following steps:

step two, firstly: and sequentially updating the resource node messages, wherein for the t iteration, the message update of the resource node k is represented as:

in the formula, r _k Represents resource block k, u _j Representing users j, x _j For SCMA coded user j's codeword, y _k For received signals on resource block k, h _kv Denotes the user gain, x, between resource k and user v _kv Code word, epsilon, representing the transmission between resource k and user v _k For a non-zero set of positions, ε, of the kth row of the factor matrix updated after t-1 iterations _k /{ i, j } denotes the slave set ε _k Excluding elements i and j, and i ≠ j, i ∈ epsilon _k ，j∈ε _k ，σ ² Is a noise variance value] ^old And 2] ^new Representing messages before and after the resource node updates the codeword message;

step two: calculating the confidence stability value of each branch according to the updated resource node message for the next iteration, wherein the message confidence stability from the resource node k to the user node j in the t-th iteration is

Wherein x is _j Representing a set of SCMA encoded codewords;

step three: the method for dynamically reducing the factor graph participating in the next iteration is characterized in that the acquired confidence stability value is preferentially propagated to branches with larger stability deviation in adjacent iterations, and the factor graph participating in the next iteration is dynamically reduced, and the method is characterized in that: in the next iteration, the branch with the highest confidence coefficient stability is removed from the factor graph, so that the branch does not participate in the next message updating of the resource node;

step four: carrying out SCMA and SCAN joint iterative detection decoding according to the dynamic factor graph;

step five: and C, performing CRC (cyclic redundancy check) on the decoded code word, if the code word passes the CRC, terminating iteration, and if the code word does not pass the CRC, returning to the step II.

2. The joint detection and decoding method of the polar code SCMA system based on pruning iteration as claimed in claim 1, wherein in said step one, said CRC encoded code word is placed at the tail end of the polar encoded code word.

3. The joint detection decoding method for the polarization code SCMA system based on pruning iteration as claimed in claim 1, wherein the message update of the resource node is performed by using an original factor graph when the message update is the first update.

4. The joint detection and decoding method of the pruning iteration based polarized code SCMA system as claimed in claim 1, wherein the step of the joint iteration detection and decoding of the fourth step comprises:

step four, firstly: obtaining a symbol message according to the updated message of the resource node, then mapping the symbol message into a bit message, and converting the bit message into a log-likelihood ratio form;

symbol message obtained according to updated message of resource node

Expressed as:

in the formula,

for the ith signal of user j, ζ _j A set of non-zero positions, t, representing the jth column of the factor matrix _max Representing the maximum number of iterations; mapping symbol messages to bit messages is calculated by the following formula:

wherein Q = log ₂ M, where M is the SCMA codeword dimension, b _j，(l-1)Q+m The [ (l-1) th Q + m ] of user j]A message of a number of bits, the number of bits,

the representation satisfies the mapping relationship:

the set of code words of (a) is,

the same can be obtained; the conversion of the bit message into a log-likelihood ratio message form can be calculated by the following equation:

then, the log-likelihood ratio message deinterleaving can be expressed as:

therein, II ^-1 Representing a de-interleaving operation;

step four and step two: de-interleaving the log-likelihood ratio message, inputting the de-interleaved log-likelihood ratio message into a polarization decoder, decoding the de-interleaved log-likelihood ratio message by adopting an SCAN algorithm, and initializing a left message and a right message of a factor graph of the SCAN algorithm; left message initialization to polarization decoded prior message

Right message

The initialization is as follows:

wherein n = log ₂ (N), N is the length of the polar code, I represents the bit set of the message, I ^C Represents a set of frozen bits;

step four and step three: the initialized left message and right message are transmitted and updated in the SCAN factor graph, and can be calculated according to the following formula:

wherein L is _s，t ，R _s，t A left message and a right message representing a user j, respectively, wherein s, t represent row and column indexes, respectively, and f (a, b) ≈ sign (a) × sign (b) × min (| a |, | b |);

step four: the left message and the right message respectively reach the leftmost end and the rightmost end of the SCAN factor graph, are interleaved and then are input into an SCMA decoder as prior messages, and the prior messages are expressed as follows:

wherein c is _j，(l-1)Q+m The (l-1) Q + m code words of user j, pi represents interleaving operation, a is weight factor

And

respectively represent

And

the mean value of (a); when the SCMA decoder receives the prior message, it is first converted into a probability message calculated by the following equation:

wherein q is _j，m E {0,1}; the probability message is then mapped to the symbol message of the SCMA decoder, denoted as:

5. the joint detection and decoding method for the polarized code SCMA system based on pruning iteration as claimed in claim 4, wherein the weighting factor a in the fourth step depends on the code rate, and when the code length N =256 and the code rate R =0.47, the weighting factor a takes a value of 0.6; when the code length N =1024 and the code rate R =0.32, the weighting factor a takes a value of 0.4.

6. The joint detection decoding method for the polarization code SCMA system based on pruning iteration as claimed in claim 1, wherein the checking method in the fifth step is to decide the message outputted from the joint detection decoding and perform CRC check on the decision result.

7. The joint detection and decoding method for the polarized code SCMA system based on pruning iteration as claimed in claim 1 or 6, wherein the verification method is to perform verification for each iteration process, and if the verification is not passed, the next iteration is performed, and the method is terminated after the maximum iteration number is reached.

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