CN114598334A

CN114598334A - Segmented CRC (cyclic redundancy check) assisted convolutional polarization code coding and decoding scheme

Info

Publication number: CN114598334A
Application number: CN202210287844.3A
Authority: CN
Inventors: 雷志明
Original assignee: Hanyin County Social Governance Intelligent Technology Co ltd
Current assignee: Hanyin County Social Governance Intelligent Technology Co ltd
Priority date: 2022-03-23
Filing date: 2022-03-23
Publication date: 2022-06-07

Abstract

The invention discloses a segmented CRC auxiliary decoding scheme based on a convolution polarization code of a sliding window algorithm, which mainly solves the problems that the complexity of the conventional SCL and CRC-SCL is very high and the performance of the conventional segmented CRC auxiliary decoding algorithm cannot be improved. The implementation scheme is as follows: 1) carrying out Monte Carlo simulation to count the error probability of each bit channel; 2) searching continuous sub-channels with highest error probability by using a sliding window algorithm; 3) performing CRC check at the subchannel which is most prone to error according to the search result of the step 2) so as to improve the retention probability of the correct path; 4) repeating the above process to add other sections of CRC in turn. 5) And carrying out convolutional polarization code coding, modulation and noise addition. 6) And carrying out segmented decoding on the received information sequence. Compared with the existing decoding algorithm, the method can reduce the calculation complexity and simultaneously has certain performance gain, and compared with the polarization code under the same condition, the method has better decoding performance.

Description

Segmented CRC (cyclic redundancy check) assisted convolutional polarization code coding and decoding scheme

Technical Field

The invention belongs to the technical field of communication, and further relates to a novel coding and decoding scheme of a convolutional polarization code assisted by segmented CRC in the technical field of wireless communication error control coding. The method can be used for channel coding under the control channel scene in a wireless communication system, can increase the polarization speed of the sub-channels, polarize more sub-channels into noise-free channels and pure noise channels, can obtain better decoding performance, and improves the reliability of information bit transmission.

Background

Convolutional polarization Codes (Convolutional Polar Codes) are new efficient coding and decoding Branch MERA Codes (Branch Multi-scale Entanglement retrieval analysis Codes) based on tensor networks proposed by Andrew James Ferris, David Poulin et al in 2014, and the equivalent forms of quantum error correction Codes and classical decoding problems and the specific definitions and structures of the Branch MERA Codes are established. Andrew James Ferris et al formally named convolutional polarization code in 2017, and provides a proof of capacity accessibility and an effective Serial Cancellation (SC) decoding algorithm. The encoding and decoding process of the convolutional polarization code comprises the following steps: firstly, determining an information set through Monte Carlo simulation; and secondly, the information bits are put on the selected channel in the information set for transmission, and the other channels transmit the frozen bits. Thirdly, coding; fourthly, transmitting through a Gaussian channel; and fifthly, performing serial cancellation decoding based on the log-likelihood ratio. However, the performance of classical SC decoding is limited, and the complexity of better-performing list decoding (SCL) and Cyclic Redundancy Check (CRC) -assisted list decoding (CRC-SCL) is too high. The main reason for the limited performance of SC decoding is that it is based on bit-by-bit decoding of already decoded bit information, and subsequent decoding will also be in error once the previously decoded bit is in error. And the SCL decoding reserves L decoding paths, and selects one with the highest reliability as a decoding result when the decoding is finished, thereby improving the decoding performance. Thus the larger L the better the performance. One problem that arises, however, is that the more paths to be preserved, the higher the computational complexity. CRC-SCL decoding is to perform CRC check on L paths when decoding is finished, the paths which pass the check are taken as decoding results, and the paths which cannot pass the check are deleted, so that the retention probability of correct paths is improved. However, it still has the problem of being too complex.

In order to reduce computational complexity, segmented CRC assisted SCL coding schemes are in force. Huayi Zhou et al propose a uniformly Segmented CRC-assisted coding scheme in its published paper "Segmented CRC-aid SC List Polar Decoding" (2016 IEEE 83rd Vehicular Technology Conference (VTC Spring),2016, pp.1-5). The method has simple principle, and the information sequence is uniformly divided into a plurality of sections in the coding process, a CRC (cyclic redundancy check) check sequence is added behind each section, and then the polarization code coding is carried out. And decoding is carried out in sequence from the first segment in the decoding process, if the current segment can pass through the CRC check, the next segment can be continuously decoded, and if the current segment cannot pass through the CRC check, the decoding is stopped, so that the decoding complexity is reduced. Although the segmentation method can effectively reduce the computational complexity, the decoding performance cannot be improved.

Disclosure of Invention

The present invention is directed to provide an non-uniform segmented CRC-assisted SCL (SCA-SCL) decoding scheme based on a sliding window algorithm, which aims to effectively reduce the computational complexity and have a certain performance gain.

In order to achieve the above object, the present invention provides a segmented CRC-assisted convolutional polarization code encoding and decoding method, which comprises the following steps:

(1) the source generates an N-bit random binary bit sequence:

the first generated N-bit binary bit sequence is used for Monte Carlo simulation, and can also send a full 0-bit sequence;

(2) determining an information set by Monte Carlo simulation:

selecting the bits with high reliability K-NR as an information set A and the other bits as a frozen bit set A from a linear code with the code length of N and the code rate of R by Monte Carlo simulation for M times^C；

(3) Generating a K-bit information bit sequence:

generating a K-bit random binary bit sequence as an information bit, and transmitting the freezing bit by the rest N-K, so that all the bits are set to be 0;

(4) searching the position of the segmentation point by using a sliding window algorithm and inserting a CRC check sequence:

firstly, selecting the length W of the sliding window as the length of CRC bit, then searching the continuous W sub-channels with the highest error times according to the error times of each bit channel estimated in (2), using the position as the position for inserting CRC bit, and proceeding to the current segmentCRC encoding the data line, and placing the obtained check sequence at the position to generate information sequence

(5) Encoding the information sequence:

based on the obtained information sequence in (4)

And (4) carrying out convolutional polarization code coding, wherein each layer has one more layer of exclusive-OR operation compared with the last layer of the polarization code. Therefore, when coding, the sub-layer coding is firstly carried out, then the conventional layer coding is carried out, and the coded bit sequence is obtained

(6) Modulating and denoising a coded sequence:

will obtain a coded bit sequence

Transmitting the signal on a Gaussian channel after Binary Phase Shift Keying (BPSK) modulation to obtain a received signal

(7) Decoding the received signal:

and still performing the SCL decoding on each segment, performing CRC (cyclic redundancy check) check after one segment decoding is finished, and if no path passes the CRC check, directly outputting a decoding failure identifier and terminating the decoding. If one of the L paths passes the CRC check, the decoding of the next segment is continued until the decoding of all segments is finished.

Compared with the prior art, the invention has the following advantages:

firstly, the segmentation method based on the sliding window algorithm is different from the traditional uniform segmentation idea, the reliability of each sub-channel is obtained according to Monte Carlo simulation, and the position of the sub-channel which is most prone to errors is searched through the sliding window algorithm. The advantage of checking at the most error prone sub-channel is that decoding can be terminated immediately upon detection of a decoding error, increasing the erasure probability of the erroneous path if the next segment is decoded without error at the most error prone position. The length of each information sequence obtained by the segmentation method is not uniformly segmented but is related to the distribution condition of the channel reliability, so that certain performance gain is obtained

Second, the present invention uses a sliding window having a length equal to the length of the CRC bit sequence, so that W consecutive channels are searched for just placing CRC bits. Simulation results show that CRC with different lengths has different checking capability, so that the lengths of the CRC added after each segment are different, and the lengths are sequentially and incrementally distributed. The reason is as follows: the first searched segment position is the position with the highest error probability in the whole sequence, so that the shorter CRC can be used as a check sequence, the second segment position is the position with the next highest error probability in the whole sequence, so that the longer CRC sequence is used for checking, and the rest of segments are performed in the same way, so that the checking capability of each segment of CRC can be fully exerted.

Thirdly, the coding scheme of the present invention is applicable not only to convolutional polar codes but also to conventional polar codes. The segmentation idea of the invention is based on the reliability distribution of the channel, so that regardless of which construction method is used, the segmentation position of the information sequence can be searched by using a sliding window algorithm as long as the reliability distribution of the sub-channel is obtained. Therefore, the method can be conveniently popularized.

Drawings

FIG. 1 is a flow diagram of an encoding implementation of the present invention;

fig. 2 is a comparison graph of a polar code and a convolutional polar code butterfly diagram taking N-8 as an example;

fig. 3 is a scatter diagram of channel capacity distribution of convolutional polarization codes and polarization codes, for example, having a code length of 1024 and an erasure probability of 0.5;

FIG. 4 is a diagram of uniform segmentation and non-uniform information sequences in the present invention;

FIG. 5 is a diagram of six decoding modes of a convolutional polarization code;

FIG. 6 is a path search diagram for SC coding and SCL coding;

FIG. 7 is a graph comparing simulation results of convolutional and polar codes under the present decoding scheme;

FIG. 8 is a graph comparing simulation results of uniform segmentation and non-uniform segmentation based on sliding window of the present invention;

FIG. 9 is a graph of average computational complexity contrast for non-segmented, uniform segmented, and non-uniform segments of a polar code and a convolutional polar code;

fig. 10 is a graph comparing simulated performance of different segment lengths of convolutional polarization codes.

Detailed Description

Embodiments and effects of the present invention will be described in detail below with reference to the accompanying drawings.

The invention relates to a non-uniform segmented SCA-SCL coding and decoding scheme based on a sliding window algorithm, which is mainly used for a channel coding module of a point-to-point wireless communication link. Referring to fig. 1, the method for implementing the encoding and decoding process of the present invention is further illustrated, which includes the following steps:

step 1, the source generates an N-bit random binary bit sequence.

And 2, determining an information set by Monte Carlo simulation.

The Monte Carlo simulation determines that the information set is related to the simulation times, the higher the precision, but the higher the complexity with the increase of the simulation times. Assuming that the code length is N and the code rate is R, it needs to determine that K ═ NR is an information bit.

And 3, generating a K-bit information bit sequence.

Suppose that the generated K is an information sequence of

And (3) according to the information bit sub-channel determined in the step (2), placing K information bits on the K information bit sub-channel, and enabling the rest bits to be 0.

And 4, searching the position of the segmentation point by using a sliding window algorithm and inserting a CRC (cyclic redundancy check) check sequence.

Determined assuming a sliding window algorithmThe information sequence of the ith segment is

Then a section of information sequence is subjected to CRC coding, assuming that the length of the obtained first CRC check sequence is r_iThen the total length of the first segment is

The lengths of the other segments are in turn available. Assuming a total of P segments, k₁+k₂+...k_i+...+k_P＝K，r₁+r₂+...+r_i+...+r_PR, then the CRC encoded sequence is

Fig. 4 is a schematic diagram of a uniform segmentation and a non-uniform segmentation information sequence obtained based on a sliding window algorithm.

And 5, carrying out convolutional polarization code encoding on the information sequence.

For (N ═ 2)^mConvolutional polarization code of K)

Wherein the generator matrix is:

wherein

F is a binary kernel matrix, T represents a transpose operation,

representing the kronecker product. In practical operation, in order to avoid repeatedly calculating the kronecker product, the recursive operation and the transpose operation in the generator matrix, the practical encoding scheme is as follows: assuming that N is 2, m layers are shared by convolutional polar codes having a code length of N, and coding of sub-layers starts from the m-th layerIs composed of

Wherein i is g · N + N/2+ j, g is 0,1,., N/N-2, j is 0,1,., N/2-1; for the conventional layer is coded as

Wherein i is g · N + j, g is 0,1,., N/N-1, j is 0,1,., N/2-1. Then, n is 2n, the coding of the m-1 th layer is performed, and so on up to the 2 nd layer. According to the butterfly structure diagram shown in fig. 2, only the first layer only needs to perform the operation of the conventional layer, and the layer omits the operation of the sub-layer, so that the coded bit sequence can be obtained

And 6, modulating and adding noise to the coding sequence.

After BPSK modulation is carried out on the coded bits, the coded bits are transmitted through a Gaussian channel, and the obtained received signal is y_i＝x_i+n_iWherein i is 0, 1.

And 7, decoding the received signal.

Segmented CRC-assisted SCL decoding mainly includes two coding modes: a decoding mode and a check mode. In the decoding mode, the decoder performs SCL decoding. In check mode, the checker checks whether the paths in the current list pass the CRC check. Wherein, SCL decoding is equivalent to that L decoders decode simultaneously and parallelly on the basis of SC decoding, and one of the L paths with the highest reliability is selected as a decoding result in the last stage. Fig. 6(a) shows SC decoding path search, and SC decoding is a special case of only one search path. Fig. 6(b) is a route search diagram illustrating an example where L is 4. The SCL decoding assisted by CRC is to perform CRC check on the L candidate paths on the basis of SCL decoding, and the paths which can pass the CRC check are taken as the final decoding result. However, both SCL decoding and SCL decoding have high computational complexity, and the complexity increases as the number of paths L increases.

The specific decoding process is as follows:

firstly, the decoder works in a decoding mode, and if the decoder decodes the data, the number of decoding paths is kept unchanged by the frozen bits; if the non-frozen bit is decoded and the current path number does not reach the set path number L, the path is directly expanded by one time, namely, each original path is decoded according to the two conditions that the current bit is 0 and 1; if the current translated bit is not frozen and the set number of paths L has been reached, pruning is also needed after the number of paths is doubled. And selecting L paths with relatively high reliability from the 2L paths, and reserving the L paths to enter the next bit for decoding.

Upon the ith CRC check sequence r_iAll bits are decoded and the decoder enters a check mode. The decoder performs a CRC check on the L paths in the list, and if the current path passes the check, the current path is retained, otherwise the current path is removed from the list. If the list is not empty, the decoder continues to go to the decoding mode and continue decoding. If no path passes the CRC check, outputting a decoding failure identifier and terminating the decoding. The above process is repeated until each segment is translated.

The wrong path in the list is deleted after each check, and only one correct path is reserved. Taking the list length L as 32 as an example, it is assumed that when the decoding of the ith non-frozen bit is completed, only one correct path is reserved after CRC check. When decoding continues to the (i +5) th non-frozen bit, 32 sub-paths of the correct path remain with probability 1. But for conventional CRC-SCL decoding, there are 1024 sub-paths when the (i +5) th non-frozen bit is decoded. When the length of the list is 1024, the correct path can be retained with probability 1. This means that in some cases, SCA-SCL decoding can implement the list length L in the list length L²The performance of (c).

The effect of the present invention is further explained by simulation experiments as follows:

simulation conditions

The parameters adopted by the simulation experiment of the invention are as follows: the Monte Carlo simulation times are 20 ten thousand, the modulation mode is BPSK modulation, the channel is an additive white Gaussian noise channel, the code length is 256, the code rate is 0.5, and the related CRC is as follows:

CRC-4	g(x)＝x⁴+x+1
		CRC-8	g(x)＝x⁸+x⁷+x⁶+x⁴+x²+1
CRC-12	g(x)＝x¹²+x¹¹+x³+x²+1
		CRC-16	g(x)＝x¹⁶+x¹²+x⁵+1
CRC-24	g(x)＝x²⁴+x²³+x⁶+x⁵+x+1

for comparative fairness, the total length of the CRC lengths is the same for all schemes.

Second, simulation content

Simulation 1, (a) and (b) of fig. 3 are channel capacity distribution diagrams of a polarization code and a convolutional polarization code having a code length of 1024 and an erasure probability of 0.5, respectively.

Simulation 2, fig. 7 is a performance comparison diagram of non-segmented, two-segmented and three-segmented polarization codes based on the SCA-SCL coding scheme proposed in the present invention. The dotted lines are simulation curves of the polarization codes, and the solid lines are simulation curves of the convolutional polarization codes.

Simulation 3, fig. 8 is a comparison graph of simulation performance of non-segmentation, uniform segmentation and the non-uniform segmentation proposed by the present invention.

Simulation 4, fig. 9 is a graph of the average computational complexity comparison result of non-segmentation, uniform segmentation and non-uniform segmentation of the polarization code and the convolutional polarization code proposed by the present invention. The dotted lines are simulation curves of the polarization codes, and the solid lines are simulation curves of the convolution polarization codes.

Simulation 5, fig. 10 is a diagram of simulation results of different combinations of non-segment lengths, with the total CRC length of the convolutional polarization code being 24.

Analysis of results

As can be seen from the channel capacity distribution shown in fig. 3, the channel polarization code degrees of the two codes are different. The convolutional polarization code polarizes more fully, it polarizes more sub-channels into a noise-free channel and a pure noise channel. Therefore, the convolutional polarization code has better decoding performance. At present, polarization codes have a plurality of construction methods, and at present, gaussian approximation with low complexity and high precision is mostly used, but monte carlo simulation is still adopted for comparing all polarization codes with convolutional polarization codes. Although the two codes are chosen to be different, both codes can be searched for segmentation points by using a sliding window algorithm. The reliability distribution is different, and the searched segment positions are naturally different.

Fig. 7 is a comparison between the performance of the non-segmented and non-uniform segmentation algorithm based on sliding window for the polar code and the convolutional polar code, and it can be seen from simulation results that both the polar code and the convolutional polar code have certain performance gain under the coding and decoding scheme of the present invention, and the performance gain increases with the increase of the number of segments. However, since CRC bits occupy some bits in the information set, the sequence added with CRC check also causes a certain loss of the code rate. All simulations are therefore guaranteed to have the same total length of CRC added.

Fig. 8 is a comparison of the performance of uniform segmentation and non-uniform segmentation of convolutional polarization codes, and it can be seen from the simulation results that the performance of both uniform segmentation and non-uniform segmentation is substantially the same, but the segmentation method of the present invention has significant gain. The tri-segment has a performance gain of about 0.2dB over non-segmented and uniform segments.

Fig. 9 is a simulation result of the average computation complexity, which is defined as the number of computations of the average path metric in the present invention. The simulation result shows that the calculation complexity is highest and constant when the segmentation is not carried out. Both uniform and non-uniform segmentation have significant complexity reduction. Compared with the uniform segmentation method, the non-uniform segmentation method has the advantages that the signal-to-noise ratio is slightly reduced at low signal-to-noise ratio, and the signal-to-noise ratio is kept equal at high signal-to-noise ratio. Furthermore, the computation complexity of convolutional polarization codes is significantly lower than that of polarization codes. The basic SC decoding of the convolutional polarization code is minimum and approximate decoding based on a log-likelihood cluster, addition and subtraction and comparison operations are used in the whole decoding calculation process to replace the original multiplication and division operation based on probability decoding, and the calculation efficiency can be obviously improved.

Fig. 10 is a simulation performance of different segment length combinations of a convolutional polar code, for example, three segments. It can be seen from the simulation results that the simulation results for different combinations of segment lengths are different, and the performance is best when the segment lengths are distributed in increments (i.e. 4, 8, 12). The simulation result also verifies that the CRC with different lengths has different checking capability in the previous analysis, so that certain performance improvement can be realized by reasonably dividing a longer CRC sequence into a plurality of different shorter CRC sequences and reasonably setting the position of each segment.

Claims

1. A segment CRC assisted SCL coding and decoding method based on a sliding window algorithm is characterized in that: using Monte Carlo simulation to obtain error probability of each sub-channel, then using sliding window to search position of segmentation point, then making CRC check, adding CRC check sequence, and making segmented decoding at receiving end by means of Gauss channel. The method comprises the following specific steps:

(1) the source generates an N-bit random binary bit sequence:

(2) determining an information set by Monte Carlo simulation:

code rate with code length of N through M Monte Carlo simulationsSelecting the bits with high reliability from the linear code of R as an information set A, and using the other bits as a frozen bit set A^C；

(3) Generating a K-bit information bit sequence:

(4) searching the position of the segmentation point by using a sliding window algorithm and inserting a CRC (cyclic redundancy check) sequence:

firstly, selecting the length W of a sliding window as the length of CRC (cyclic redundancy check) bit, then searching the continuous W sub-channels with the highest error times according to the error times of each bit channel estimated in the step (2), taking the position as the position for inserting the CRC bit, carrying out CRC (cyclic redundancy check) coding on the current segment, and placing the obtained check sequence at the position, thereby generating an information sequence

(5) Encoding the information sequence:

based on the obtained information sequence in (4)

Convolutional polarization code encoding is carried out, and compared with the last layer of the polarization code, the convolutional polarization code has the advantage that the XOR operation of one sublayer is added to each layer; therefore, when coding, the sub-layer coding is firstly carried out, then the conventional layer coding is carried out, and the coded bit sequence is obtained

(6) Modulating and denoising a coded sequence:

will obtain a coded bit sequence

(7) Decoding the received signal:

2. The method of claim 1, wherein: (4) searching segmentation points by using a sliding window, searching a continuous sub-channel which is most prone to error, performing CRC (cyclic redundancy check) at a position which is most tolerant to error, and increasing the deletion probability of an error path; the method comprises the following specific steps:

firstly, Monte Carlo simulation is carried out to obtain the error probability of each subchannel. Selecting a K-NR sub-channel with higher reliability according to the code length N and the code rate R;

secondly, according to K sub-channels selected in the last step, a sliding window algorithm is implemented, the first selected sub-channel is calculated to the last sub-channel, and the continuous sub-channel with the largest error frequency obtained by the first calculation is obtained; carrying out the sliding window algorithm again from the position of the first found segmentation point to the back for the second time to find a second segmentation point; finding other segmentation points by analogy;

and thirdly, performing CRC coding on each subsequence to obtain a CRC check sequence, and adding the CRC check sequence.

3. The method of claim 1, wherein: (5) the coding in (1) is not to directly use a generating matrix to code an information sequence, but to code the sub-layer and the conventional layer according to the characteristic that the convolutional polarization code has two layers of polarization; for m layers of the convolutional polarization code with the code length of N, and the control parameter N of the initialization sublayer is 2, the specific operation steps are as follows:

in a first step, the sub-layer is encoded first, starting from the m-th layer, into

Wherein i is g · N + N/2+ j, g is 0,1,., N/N-2, j is 0,1,., N/2-1;

a second step of encoding the conventional layer as

Wherein i is g.n + j, g is 0, 1., N/N-1, j is 0, 1., N/2-1;

and thirdly, enabling n to be 2n, carrying out coding on the m-1 layer, and so on until the 2 nd layer. According to the butterfly structure diagram shown in fig. 2, only the first layer only needs to perform the operation of the conventional layer, and the layer omits the operation of the sub-layer, so that the coded bit sequence can be obtained

4. The method of claim 1, wherein: (7) the SC decoding based on the middle-segment decoding uses the minimum and approximate decoding based on the log-likelihood cluster to replace the numerical unstable probability-based decoding, and in addition, the segment decoding process has two modes, namely a decoding mode and a checking mode; the specific operation steps are as follows:

firstly, decoding log-likelihood clusters based on six modes in a basic SC decoding process. Firstly, initializing a first layer of log-likelihood clusters according to a received signal;

secondly, decoding is started layer by layer from the second layer to the mth layer; when the last layer is translated, three cases occur: in the first case, three bits of the current three clusters are unknown, and at the moment, the two unknown bits need to be traversed to obtain the log-likelihood ratio of the current bit, and then hard decision decoding is carried out; in the second case, one bit is known and two bits are unknown in the current three clusters, and at this time, the known bit is used as prior information to traverse the last bit to obtain the log-likelihood ratio of the current bit, and then hard decision is performed; in the third situation, the first two bits are known, and at this time, the first two bits are used as prior information to obtain the log-likelihood ratio of the current bit, and then hard decision decoding is carried out;

thirdly, the bit needs to be updated reversely every time a bit is decoded, which is very similar to the polarization code, but the updating modes are slightly different due to different structures of the two bits;

fourthly, when the last bit of the CRC sequence is not decoded, a decoding mode is executed all the time, namely the decoding process of the first three steps; in addition, the path is required to be processed after one bit is translated every time, if the frozen bit is translated to keep the number of the decoding paths unchanged, if the non-frozen bit is translated and the current path number does not reach the set path number L, the path is directly expanded by one time, namely, each original path is decoded according to two conditions that the current bit is 0 and 1, and if the non-frozen bit is translated and the set path number L is reached, the path number is required to be pruned after the path number is expanded by one time; selecting L paths with relatively high reliability from the 2L paths, reserving the L paths, and entering next-bit decoding;

fifthly, when the last bit of the CRC sequence is decoded, entering a check mode, and comparing the CRC check sequence obtained by decoding with the check sequence before encoding; if the two are equal, the CRC can be passed, otherwise, the decoding is error, the decoding failure mark is output, and the decoding is stopped, so that the calculation complexity is reduced, and the computer resources are saved.