CN108282264B - A Polar Code Decoding Method Based on Bit Flip Serial Elimination List Algorithm - Google Patents

A Polar Code Decoding Method Based on Bit Flip Serial Elimination List Algorithm Download PDF

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CN108282264B
CN108282264B CN201810010667.8A CN201810010667A CN108282264B CN 108282264 B CN108282264 B CN 108282264B CN 201810010667 A CN201810010667 A CN 201810010667A CN 108282264 B CN108282264 B CN 108282264B
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相征
孙五星
任鹏
刘明辉
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Xian University of Electronic Science and Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
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    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
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    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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Abstract

The invention discloses a polarization code decoding method based on a bit reversal serial elimination list algorithm, which solves the problem that the traditional SCL algorithm has higher time complexity and comprises the steps of (1) receiving a sequence to be decoded by a communication terminal, (2) carrying out SC decoding on the received sequence to be decoded, (3) judging whether the SC decoding sequence passes CRC (cyclic redundancy check), initializing the list width and the bit reversal times, (5) selecting a judgment error position set, (6) selecting elements from the judgment error position set, (7) carrying out decoding by using the bit reversal serial elimination list algorithm, (8) judging whether the elements in the judgment error position set are selected, (9) successfully decoding, (10) failing decoding, combining bit reversal and list decoding to carry out re-decoding when the decoding fails, thereby improving the decoding performance and reducing the time complexity of the decoding algorithm.

Description

基于比特翻转串行消除列表算法的极化码译码方法A Polar Code Decoding Method Based on Bit Flip Serial Elimination List Algorithm

技术领域technical field

本发明属于通信技术领域，更进一步涉及信道编码技术领域中一种基于比特翻转串行消除列表算法的极化码译码方法。本发明可用于对遥感图像传输、通信卫星传输以及第五代移动通信等各种通信系统中，对要发送的信源信息进行极化码编码，然后用本发明中的极化码译码方法解码，以纠正由于信道噪声造成的传输差错。The invention belongs to the technical field of communication, and further relates to a polar code decoding method based on a bit-flip serial elimination list algorithm in the technical field of channel coding. The present invention can be used in various communication systems such as remote sensing image transmission, communication satellite transmission, and fifth-generation mobile communications, etc., to perform polar code encoding on the source information to be sent, and then use the polar code decoding method in the present invention. Decoding to correct transmission errors due to channel noise.

背景技术Background technique

极化码因其在理论上被证明可以达到香农极限,并且具有较低的编译码计算复杂度,有确定性的构造方法，使其可以用于上述通信系统中信道编码方案，以此解决信息在无线信道中传输差错问题。Polar codes are theoretically proven to reach the Shannon limit, and have low computational complexity for encoding and decoding, and a deterministic construction method, which makes them suitable for channel coding schemes in the above communication systems to solve information problems. Transmission error problems in wireless channels.

现有极化码的串行消除SC(Successive Cancellation)译码方法是基于似然比(likelihood ratio,LR)逐比特顺序译码。虽然串行消除SC译码在码长N很长的情况下能够获得很好的渐近性能，逼近香农限。但是当码长N较短或者中等长度的时，由于Polar码仍然还有部分没极化的信道，在这些没极化的信道传输信息比特，很容易导致译码出错。其次，串行消除SC译码方法在译码过程中会产生错误传播，使其性能没有超过Turbo码和低密度奇偶校验LDPC(Low-density Parity-check)码的性能，还需要进一步提高译码性能。The existing serial cancellation SC (Successive Cancellation) decoding method of polar codes is based on the likelihood ratio (Likelihood ratio, LR) decoding bit by bit sequence. Although serial-elimination SC decoding can obtain good asymptotic performance when the code length N is very long, it is close to the Shannon limit. However, when the code length N is short or medium, since the Polar code still has some unpolarized channels, it is easy to cause decoding errors to transmit information bits in these unpolarized channels. Secondly, the serial elimination SC decoding method will cause error propagation in the decoding process, so that its performance does not exceed the performance of Turbo codes and Low-density Parity-check (LDPC) codes, and it is necessary to further improve the decoding performance. code performance.

ORION A,BALATSOUKAS-STIMMING A,ANDREAS B.在其发表的论文“A Low-complexity Improved Successive Cancellation Decoder for Polar Codes”([C]//Proceedings of IEEE 48th Asilomar Conference on Signals,Systems andComputers.Pacific Grove:IEEE,2014:2116-2120.)中公开了一种极化码译码方法。该译码方法首先进行串行消除SC译码，在串行消除SC译码算法输出结果不能通过循环冗余校验CRC(Cyclic Redundancy Check)时，该译码方法根据信息位对应的对数似然比的绝对值

Figure GDA0002265545590000011
来选取T个最小判定位以此作为不可靠信息位的估计，并将这些位对应的索引值构成集合M。每次从集合M中取出一个值，然后重新执行串行消除SC算法译码，并对判定序列
Figure GDA0002265545590000012
中该索引标志对应的不可靠的信息位进行比特翻转，将翻转结果作为该索引位置的译码结果。如果新的码字估值
Figure GDA0002265545590000021
通过循环冗余校验，则译码成功，否则选择M集合中下一位索引值，继续进行上述过程。遍历集合M后如仍未得到有效码字，则译码失败。该译码方法在译码性能上得到了一定程度的提升，相比于串行消除列表SCL(Successive CancellationList)译码方法大大减少了时间复杂度。但是，该方法仍然存在的不足之处是：每次只尝试翻转一次不可靠信息位，译码性能不好，无法用于性能要求高的通信系统。ORION A, BALATSOUKAS-STIMMING A, ANDREAS B. In their paper "A Low-complexity Improved Successive Cancellation Decoder for Polar Codes" ([C]//Proceedings of IEEE 48th Asilomar Conference on Signals, Systems and Computers. Pacific Grove: A polar code decoding method is disclosed in IEEE, 2014:2116-2120.). The decoding method first performs serial elimination SC decoding. When the output result of the serial elimination SC decoding algorithm cannot pass the Cyclic Redundancy Check (CRC), the decoding method is based on the logarithm similarity corresponding to the information bits. the absolute value of the ratio
Figure GDA0002265545590000011
To select T minimum decision bits as the estimation of unreliable information bits, and form a set M of index values corresponding to these bits. Each time a value is taken from the set M, and then the serial elimination SC algorithm decoding is re-executed, and the decision sequence is
Figure GDA0002265545590000012
The unreliable information bits corresponding to the index flag are bit-flipped, and the flipping result is used as the decoding result of the index position. If the new codeword is estimated
Figure GDA0002265545590000021
If the cyclic redundancy check is passed, the decoding is successful; otherwise, the next index value in the M set is selected, and the above process is continued. If no valid codeword is obtained after traversing the set M, the decoding fails. The decoding performance has been improved to a certain extent, and the time complexity is greatly reduced compared with the SCL (Successive Cancellation List) decoding method. However, this method still has the disadvantage that it only tries to flip the unreliable information bit once each time, and the decoding performance is not good, so it cannot be used in a communication system with high performance requirements.

西安电子科技大学在申请的专利文献“一种基于比特翻转的串行列表译码算法”(申请公布日：2016年9月28日，申请公布号：CN 105978557A)中公开了一种基于比特翻转的串行列表译码算法。该发明实施例针对极化码，提出了一种新的基于比特翻转的串行列表译码算法。该算法针对循环冗余校验辅助的串行抵消列表CA-SCL译码算法(CyclicRedundancy Check Aid Successive Cancellation List)中的错误传播问题，把原错误路径上第一次出现的错误比特进行翻转，使之变为正确的路径。和循环冗余校验辅助的串行抵消列表CA-SCL算法相比，该译码算法在性能上有了较大的提升，保证安全性的同时，提高了便利性。但是，该方法仍然存在的不足之处是，该译码算法是以增加译码复杂度为代价来提升译码性能，即使在高信噪比环境下，该译码复杂度仍然很高，无法用于实际的通信系统中。In the patent document "A Serial List Decoding Algorithm Based on Bit Flip" (application publication date: September 28, 2016, application publication number: CN 105978557A), Xi'an University of Electronic Science and Technology disclosed a kind of bit flip-based decoding algorithm. The serial list decoding algorithm. This embodiment of the invention proposes a new serial list decoding algorithm based on bit flipping for polar codes. Aiming at the error propagation problem in the Cyclic Redundancy Check Aid Successive Cancellation List (Cyclic Redundancy Check Aid Successive Cancellation List) decoding algorithm, the algorithm flips the first error bit on the original error path to make becomes the correct path. Compared with the serial cancellation list CA-SCL algorithm assisted by the cyclic redundancy check, the decoding algorithm has a great improvement in performance, which ensures the security and improves the convenience. However, the disadvantage of this method is that the decoding algorithm improves the decoding performance at the expense of increasing the decoding complexity. Even in a high signal-to-noise ratio environment, the decoding complexity is still very high and cannot be used in actual communication systems.

发明内容SUMMARY OF THE INVENTION

本发明的目的在于针对上述已有技术的不足，提出一种基于比特翻转串行消除列表算法的极化码译码方法，提高了极化码的译码性能，同时具有相对较低的复杂度，在高信噪比环境下，本发明的译码方法的时间复杂度逐渐趋于串行消除SC算法的复杂度。The purpose of the present invention is to provide a polar code decoding method based on the bit-flip serial elimination list algorithm in view of the deficiencies of the above-mentioned prior art, which improves the decoding performance of polar codes and has relatively low complexity at the same time. , in a high signal-to-noise ratio environment, the time complexity of the decoding method of the present invention gradually tends to the complexity of the serial elimination SC algorithm.

为实现上述目的，本发明的技术思路是：首先对极化码进行串行消除SC译码，若译码结果能够通过循环冗余校验，则直接输出正确结果。否则利用判决层中信息位对应的极化信道的对数似然比值LLR(Log Likelihood Ratio)的绝对值找出判决可能出错的位置。然后开始进行比特翻转的串行消除列表译码，当译码进行到判决可能出错位置处时，直接将SC译码序列中该判决出错位置对应的比特进行反转来作为此次该位置的译码结果，继续进行余下的译码直至进行到译码树中的叶子节点处，当候选路径中有一个能通过循环冗余校验时，则译码结束，否则重新从判决可能出错位置集中选出下一个元素重新执行比特翻转的串行消除列表译码。In order to achieve the above object, the technical idea of the present invention is as follows: first, perform serial elimination SC decoding on the polar code, and directly output the correct result if the decoding result can pass the cyclic redundancy check. Otherwise, use the absolute value of the log-likelihood ratio LLR (Log Likelihood Ratio) of the polarized channel corresponding to the information bit in the decision layer to find out the position where the decision may be wrong. Then start the serial elimination list decoding of bit flipping. When the decoding progresses to the position where the judgment may be wrong, directly invert the bit corresponding to the wrong position of the judgment in the SC decoding sequence as the decoding of this position. If one of the candidate paths can pass the cyclic redundancy check, then the decoding ends, otherwise, it will be re-selected from the set of possible errors in the judgment. Re-execute the bit-flipped serial elimination list decoding for the next element.

本发明的实现步骤如下：The implementation steps of the present invention are as follows:

(1)从通信终端接收待译码序列：(1) Receive the sequence to be decoded from the communication terminal:

(2)对待译码序列先进行串行消除SC译码：(2) First perform serial elimination SC decoding on the sequence to be decoded:

(2a)计算极化信道的对数似然比值；(2a) Calculate the log-likelihood ratio of the polarized channel;

(2b)根据译码结构判决层中信息位对应的每一个极化信道的对数似然比值的正负对通信终端收到的序列进行判决，若为正，判决为0，为负则判决为1，对于通信终端收到的序列中每一个非信息位对应的位置比特，直接判决为0；(2b) Determine the sequence received by the communication terminal according to the positive and negative log-likelihood ratios of each polarized channel corresponding to the information bits in the decoding structure decision layer. If it is positive, the decision is 0, and if it is negative, the decision is made. is 1, and the position bit corresponding to each non-information bit in the sequence received by the communication terminal is directly judged to be 0;

(2c)判断当前译码序列的序号是否大于极化码的码长，若是，则将当前译码序列作为串行消除SC译码序列后执行步骤(3)，否则，将当前译码序列的序号加1后执行步骤(2a)；(2c) Judging whether the serial number of the current decoding sequence is greater than the code length of the polar code, if so, then use the current decoding sequence as the serial elimination SC decoding sequence and then execute step (3), otherwise, use the current decoding sequence Step (2a) is executed after the serial number is incremented by 1;

(3)判断串行消除SC译码序列是否通过循环冗余CRC校验，若是，则执行步骤(9)，否则，执行步骤(4)：(3) judge whether the serial elimination SC decoding sequence passes the cyclic redundancy CRC check, if yes, then execute step (9), otherwise, execute step (4):

(4)用一个2的整数次方的值，初始化串行消除列表算法的列表宽度和比特翻转次数；(4) Initialize the list width and the number of bit flips of the serial elimination list algorithm with a value of an integer power of 2;

(5)选取判决出错的位置集：(5) Select the position set where the judgment is wrong:

按照从小到大的排序方法，依次从未通过循环冗余CRC校验的串行消除SC译码序列中，选取信息位集所对应的译码判决出错的位置，将所有出错的位置构成串行消除SC译码判决出错的位置集；According to the sorting method from small to large, from the serial elimination SC decoding sequence that has not passed the cyclic redundancy CRC check, select the position of the decoding judgment error corresponding to the information bit set, and form all the wrong positions into a serial Eliminate the wrong position set of SC decoding decision;

(6)依次从串行消除SC译码判决出错的位置集中选出一个元素；(6) select an element successively from the position set where the error of the SC decoding decision is eliminated serially;

(7)利用比特翻转串行消除列表算法进行译码：(7) Use the bit-flip serial elimination list algorithm to decode:

(7a)判断当前译码序列的序号是否等于所选出错位置集元素的值，若是，则执行步骤(7b)，否则，执行步骤(7c)；(7a) judge whether the sequence number of the current decoding sequence is equal to the value of the selected error position set element, if so, execute step (7b), otherwise, execute step (7c);

(7b)按照下式，按照下式，使用惩罚因子计算译码树中每一个译码序号等于译码判决出错的位置集中的元素值处的每一个扩展路径的度量值，以间接实现比特翻转；(7b) According to the following formula, according to the following formula, use the penalty factor to calculate the metric value of each extension path where each decoding sequence number in the decoding tree is equal to the element value in the position set where the decoding decision is wrong, so as to indirectly realize bit flipping ;

Figure GDA0002265545590000031
Figure GDA0002265545590000031

其中，

Figure GDA0002265545590000032
表示译码树中由第1位译码比特u1到第i位译码比特ui，所构成的扩展路径的度量值，
Figure GDA0002265545590000033
表示译码树中由第1位译码比特u1到第i-1位译码比特ui-1，所构成的扩展路径的度量值，ue表示串行消除SC译码序列中第e位所对应的比特值，e表示从串行消除SC译码判决出错位置集中选出的元素值，Li表示译码结构判决层中第i位极化信道对数似然比值的绝对值，α表示惩罚因子，其取值范围为100≤α≤2000；in,
Figure GDA0002265545590000032
represents the metric value of the extension path formed by the first decoding bit u 1 to the i-th decoding bit u i in the decoding tree,
Figure GDA0002265545590000033
Represents the metric value of the extension path formed by the first decoding bit u 1 to the i-1 bit decoding bit u i-1 in the decoding tree, and u e represents the e-th decoding sequence in the serial elimination SC decoding sequence. The bit value corresponding to the bit, e represents the element value selected from the set of error positions in the serial elimination SC decoding decision, Li represents the absolute value of the log-likelihood ratio of the i -th polarized channel in the decoding structure decision layer, α represents the penalty factor, and its value range is 100≤α≤2000;

(7c)按照下式，计算译码树中每一个译码序列的序号处的每一个扩展路径的度量值；(7c) according to the following formula, calculate the metric value of each extension path at the sequence number of each decoding sequence in the decoding tree;

Figure GDA0002265545590000041
Figure GDA0002265545590000041

其中，表示译码树中由第1位译码比特u1到第i位译码比特ui，所构成的扩展路径的度量值，

Figure GDA0002265545590000043
表示译码树中由第1位译码比特u1到第i-1位译码比特ui-1，所构成的扩展路径的度量值，∈表示属于操作，Λ表示编码时选出的信息位集，b表示正确的冻结比特值，其值为0，Li表示判决层中第i位极化信道的对数似然比值的绝对值；in, represents the metric value of the extension path formed by the first decoding bit u 1 to the i-th decoding bit u i in the decoding tree,
Figure GDA0002265545590000043
Represents the metric value of the extension path formed by the first decoding bit u 1 to the i-1 bit decoding bit u i-1 in the decoding tree, ∈ indicates that it belongs to the operation, and Λ indicates the information selected during encoding Bit set, b represents the correct frozen bit value, and its value is 0, and Li represents the absolute value of the log-likelihood ratio of the i -th polarized channel in the decision layer;

(7d)判断扩展路径的度量值是否小于等于串行消除列表算法的列表宽度值，若是，则执行步骤(7e)，否则，执行步骤(7f)；(7d) judge whether the metric value of the extension path is less than or equal to the list width value of the serial elimination list algorithm, if so, execute step (7e), otherwise, execute step (7f);

(7e)保留所有扩展路径；(7e) All extension paths are reserved;

(7f)对扩展路径的度量值进行从大到小排序，将排序中的前Q条扩展路径作为候选路径，其中Q取值等于串行消除列表算法的列表宽度值；(7f) sorting the metric values of the extended paths from large to small, and using the first Q extended paths in the sorting as candidate paths, where the value of Q is equal to the list width value of the serial elimination list algorithm;

(7g)判断当前译码序列的序号是否大于极化码的码长，若是，则执行步骤(7h)，否则，将当前译码序列的序号加1后执行步骤(7a)；(7g) judge whether the serial number of the current decoding sequence is greater than the code length of the polar code, if so, execute step (7h), otherwise, execute step (7a) after adding 1 to the serial number of the current decoding sequence;

(7h)判断候选路径中是否有通过循环冗余校验的路径，若是，从通过循环冗余检验的候选路径中选取路径度量最大的一条路径作为译码序列后执行步骤(9)，否则，执行步骤(8)；(7h) determine whether there is a path that passes the cyclic redundancy check in the candidate paths, if so, select a path with the largest path metric from the candidate paths that pass the cyclic redundancy check as the decoding sequence and execute step (9), otherwise, Execute step (8);

(8)判断是否选取完串行消除SC译码判决出错的位置集中的所有元素，若是，则执行步骤(10)，否则，执行步骤(6)；(8) judge whether to select all the elements in the position set where the serial elimination SC decoding decision made an error, if so, execute step (10), otherwise, execute step (6);

(9)译码成功，输出译码成功的序列；(9) Decoding is successful, and the sequence of successful decoding is output;

(10)译码失败，输出串行消除SC译码序列。(10) The decoding fails, and the serial elimination SC decoding sequence is output.

本发明与现有技术相比具有以下优点：Compared with the prior art, the present invention has the following advantages:

第一，由于本发明使用惩罚因子，计算译码树中每一个译码序号等于译码判决出错的位置集中的元素值处的每一个扩展路径的度量值，以间接实现比特翻转，克服了现有技术中的单比特翻转串行消除译码算法每次只尝试翻转一次不可靠信息位，译码性能不好，无法用于性能要求高的通信系统的问题，使得本发明通过使用串行消除列表译码算法，明显提高了译码的纠错性能。First, because the present invention uses the penalty factor, the metric value of each extension path at the element value in the position set where each decoding sequence number in the decoding tree is equal to the error of the decoding decision is calculated, so as to indirectly realize the bit flip and overcome the current situation. The single-bit flip serial elimination decoding algorithm in the prior art only tries to flip the unreliable information bit once each time, the decoding performance is not good, and the problem that it cannot be used in a communication system with high performance requirements makes the present invention use serial elimination. The list decoding algorithm significantly improves the error correction performance of the decoding.

第二，由于本发明对待译码序列先进行串行消除SC译码，当串行消除SC译码序列没有通过循环冗余CRC校验时，再利用比特翻转串行消除列表算法进行译码，克服了现有技术中的基于比特翻转的串行列表译码算法以增加译码复杂度为代价来提升译码性能，即使在高信噪比环境下，该译码复杂度仍然很高，无法用于实际的通信系统中的问题，使得本发明实现了在高信噪比下，译码复杂度逐渐趋于串行消除SC的复杂度，明显降低译码算法的时间复杂度。Second, since the sequence to be decoded in the present invention first performs serial elimination SC decoding, when the serial elimination SC decoding sequence fails the cyclic redundancy CRC check, the bit-flip serial elimination list algorithm is used for decoding, It overcomes the fact that the serial list decoding algorithm based on bit flip in the prior art improves the decoding performance at the expense of increasing the decoding complexity. Even in a high signal-to-noise ratio environment, the decoding complexity is still very high and cannot be used. The problem in the actual communication system makes the present invention realize that under high signal-to-noise ratio, the decoding complexity gradually tends to serially eliminate the SC complexity, and the time complexity of the decoding algorithm is obviously reduced.

附图说明Description of drawings

图1为本发明的流程图；Fig. 1 is the flow chart of the present invention;

图2为改进的译码算法SFSCL与现有串行消除SC、循环冗余校验辅助的串行消除列表CRC-SC、基于单比特翻转串行消除SFSC译码方法的误帧率曲线对比图；Figure 2 is a comparison diagram of the frame error rate curve between the improved decoding algorithm SFSCL and the existing serial elimination SC, the cyclic redundancy check-assisted serial elimination list CRC-SC, and the single-bit flip serial elimination SFSC decoding method ;

图3为改进的译码算法SFSCL与现有SC，CRC-SCL，SFSC译码方法的归一化的平均译码复杂度曲线对比图。FIG. 3 is a comparison diagram of the normalized average decoding complexity curve between the improved decoding algorithm SFSCL and the existing SC, CRC-SCL, and SFSC decoding methods.

具体实施方式Detailed ways

下面结合附图对本发明做进一步描述。The present invention will be further described below with reference to the accompanying drawings.

参照附图1，对本发明的具体步骤做进一步描述。Referring to Figure 1, the specific steps of the present invention will be further described.

步骤1，从通信终端接收待译码序列。Step 1: Receive the sequence to be decoded from the communication terminal.

步骤2，对待译码序列进行串行消除SC译码。Step 2: Perform serial elimination SC decoding on the sequence to be decoded.

计算极化信道的对数似然比值。Calculate the log-likelihood ratio of the polarized channel.

根据极化信道序号的奇偶分别计算译码结构判决层中极化信道的对数似然比值：Calculate the log-likelihood ratio of the polar channel in the decision layer of the decoding structure according to the parity of the polar channel number:

按照下式，计算译码结构判决层中每个序号为奇数的极化信道的对数似然比值；According to the following formula, calculate the log-likelihood ratio of each odd-numbered polar channel in the decoding structure decision layer;

Figure GDA0002265545590000051
Figure GDA0002265545590000051

其中，

Figure GDA0002265545590000052
表示极化码编码后的码字长度为N的译码结构判决层中第k个奇数序号的极化信道输入为的极化信道对数似然比值，k表示译码结构判决层中极化信道的序号，其取值为2j-1，且1≤j≤N/2，N表示极化码编码后的码字长度，
Figure GDA0002265545590000062
表示该极化信道的输入，y表示通信终端收到的序列,
Figure GDA0002265545590000063
表示已经译出的前k-1位码字序列，sign(·)表示一个当L1与L2的乘积为正数时，函数值为1,当L1与L2的乘积为负数时，函数值为-1的函数，L1表示译码结构邻近层中上分支的极化信道对数似然比，L2表示译码结构邻近层中下分支的极化信道的对数似然比值，min(·)表示求两个实数中最小值的函数，|·|表示求绝对值操作。in,
Figure GDA0002265545590000052
The polar channel input of the k-th odd serial number in the decision layer of the decoding structure with the codeword length of N after polar code encoding is: The log-likelihood ratio of the polarized channel, k represents the sequence number of the polarized channel in the decision layer of the decoding structure, and its value is 2j-1, and 1≤j≤N/2, N represents the code encoded by the polar code word length,
Figure GDA0002265545590000062
represents the input of the polarized channel, y represents the sequence received by the communication terminal,
Figure GDA0002265545590000063
Represents the decoded first k-1 bit codeword sequence, sign( ) represents a function value of 1 when the product of L 1 and L 2 is positive, and when the product of L 1 and L 2 is negative, The function value is -1, L 1 represents the log-likelihood ratio of the polarized channel of the upper branch in the adjacent layer of the decoding structure, L 2 represents the log-likelihood ratio of the polarized channel of the lower branch in the adjacent layer of the decoding structure , min(·) represents the function of finding the minimum value of two real numbers, and |·| represents the operation of finding the absolute value.

按照下式，计算译码结构判决层中每个序号为偶数的极化信道的对数似然比值。According to the following formula, the log-likelihood ratio of each polar channel with an even number in the decoding structure decision layer is calculated.

其中，

Figure GDA0002265545590000065
表示极化码编码后的码字长度为N的译码结构判决层中第m个偶数序号的极化信道输入为
Figure GDA0002265545590000066
的极化信道对数似然比值，m表示译码结构判决层中极化信道的序号，其取值为2j，且1≤j≤N/2，N表示极化码编码后的码字长度，
Figure GDA0002265545590000067
表示该极化信道的输入，y表示通信终端的接收端收到的序列，
Figure GDA0002265545590000068
表示已经译出的前m-1位码字序列，
Figure GDA0002265545590000069
表示已经译出的第m-1位码字。in,
Figure GDA0002265545590000065
The polar channel input of the m-th even number in the decision layer of the decoding structure with the codeword length of N after polar code encoding is:
Figure GDA0002265545590000066
The log-likelihood ratio of the polarized channel, m represents the sequence number of the polarized channel in the decision layer of the decoding structure, and its value is 2j, and 1≤j≤N/2, N represents the codeword length after polar code encoding ,
Figure GDA0002265545590000067
represents the input of the polarized channel, y represents the sequence received by the receiving end of the communication terminal,
Figure GDA0002265545590000068
Represents the first m-1 bit codeword sequence that has been decoded,
Figure GDA0002265545590000069
Indicates the m-1th codeword that has been decoded.

根据译码结构判决层中信息位对应的每一个极化信道的对数似然比值的正负对通信终端收到的序列进行判决，若为正，判决为0，为负则判决为1，对于通信终端收到的序列中每一个非信息位对应的位置比特，直接判决为0。当译码进行到最后一位时，最终得出串行消除SC译码序列。The sequence received by the communication terminal is judged according to the positive and negative of the log-likelihood ratio of each polarized channel corresponding to the information bit in the decoding structure decision layer. If it is positive, the decision is 0; The position bit corresponding to each non-information bit in the sequence received by the communication terminal is directly judged to be 0. When the decoding proceeds to the last bit, the serial elimination SC decoding sequence is finally obtained.

其中，对于信息位对应的比特，按照下式进行判决。Among them, the bits corresponding to the information bits are determined according to the following formula.

Figure GDA00022655455900000610
Figure GDA00022655455900000610

其中，

Figure GDA00022655455900000611
表示译码序列中第i位译码比特值，
Figure GDA00022655455900000612
表示判决层中第i位极化信道的对数似然比值，Λ表示信息位集。in,
Figure GDA00022655455900000611
represents the i-th decoded bit value in the decoded sequence,
Figure GDA00022655455900000612
represents the log-likelihood ratio of the i-th polarized channel in the decision layer, and Λ represents the information bit set.

信息位集Λ按下面的方式进行选取：The information bit set Λ is selected as follows:

根据高斯近似计算极化信道的均值

Figure GDA0002265545590000071
Calculate the mean value of the polarized channel according to the Gaussian approximation
Figure GDA0002265545590000071

对于(N,k)极化码从N个信道中挑选出k个信道用于信息传输，信息位的选取是极化码的关键。本发明采用高斯近似来对极化信道进行可靠性估计。即在BAWGN信道下，可以将密度进化中的LLR值的概率密度函数用一簇方差为均值2倍的高斯分布来去近似。对噪声方差为σ2高斯白信道AWGN，接收端获取的接收信号为y：For (N,k) polar codes, k channels are selected from N channels for information transmission, and the selection of information bits is the key to polar codes. The present invention uses Gaussian approximation to estimate the reliability of the polarized channel. That is, under the BAWGN channel, the probability density function of the LLR value in the density evolution can be approximated by a cluster of Gaussian distributions whose variance is twice the mean. For the noise variance σ 2 Gaussian white channel AWGN, the received signal obtained by the receiver is y:

y＝(1-2x)+zy=(1-2x)+z

其中，y表示接收端接收到的序列，x表示发送比特，x∈{0,1}，z表示均值为0，方差为σ2高斯白噪声，信源比特序列采用BPSK调制，其概率密度函数为：Among them, y represents the sequence received by the receiver, x represents the transmitted bit, x∈{0,1}, z represents the mean value of 0, the variance is σ 2 Gaussian white noise, the source bit sequence is modulated by BPSK, and its probability density function for:

Figure GDA0002265545590000072
Figure GDA0002265545590000072

其中，p(y|x)表示发送端发送x，接收端收到y的概率密度函数，σ2表示高斯白噪声的方差。Among them, p(y|x) represents the probability density function that the sender sends x and the receiver receives y, and σ 2 represents the variance of white Gaussian noise.

假设发送的比特为全零序列，则对应的LLR值为Assuming that the transmitted bits are all zero sequences, the corresponding LLR value is

其中，LLR(y)表示信道层的极化信道的对数似然比值，ln(·)表示自然对数操作，p(·|·)表示信道层的转移概率，y表示接收端接收到的序列，σ2表示高斯白噪声的方差。Among them, LLR(y) represents the log-likelihood ratio of the polarized channel of the channel layer, ln( ) represents the natural logarithm operation, p( | ) represents the transition probability of the channel layer, and y represents the received sequence, σ 2 represents the variance of white Gaussian noise.

根据密度进化中的设定，令

Figure GDA0002265545590000074
表示的概率密度函数，那么
Figure GDA0002265545590000076
也是服从
Figure GDA00022655455900000710
的高斯分布。再根据高斯近似的构造理论，将密度进化的计算转化为对均值
Figure GDA0002265545590000077
的递归计算：According to the settings in density evolution, let
Figure GDA0002265545590000074
express The probability density function of , then
Figure GDA0002265545590000076
also obey
Figure GDA00022655455900000710
Gaussian distribution. Then, according to the construction theory of Gaussian approximation, the calculation of density evolution is converted into pair mean
Figure GDA0002265545590000077
The recursive calculation of :

当判决层中极化信道的序号为奇数时，按下式计算其均值 When the sequence number of the polarized channel in the decision layer is odd, the mean value is calculated as follows

Figure GDA0002265545590000079
Figure GDA0002265545590000079

其中，

Figure GDA0002265545590000081
表示判决层中第2i-1个极化信道的概率密度函数的均值，
Figure GDA0002265545590000082
表示邻近层中极化信道的概率密度函数的均值，
Figure GDA0002265545590000083
表示
Figure GDA0002265545590000084
的反函数，
Figure GDA0002265545590000085
定义如下：in,
Figure GDA0002265545590000081
represents the mean of the probability density function of the 2i-1th polarized channel in the decision layer,
Figure GDA0002265545590000082
represents the mean of the probability density functions of polarized channels in adjacent layers,
Figure GDA0002265545590000083
express
Figure GDA0002265545590000084
the inverse function of ,
Figure GDA0002265545590000085
Defined as follows:

Figure GDA0002265545590000086
Figure GDA0002265545590000086

当判决层中极化信道的序号为偶数时，按下式计算其均值

Figure GDA0002265545590000087
When the sequence number of the polarized channel in the decision layer is an even number, the mean value is calculated as follows
Figure GDA0002265545590000087

其中，

Figure GDA0002265545590000089
表示判决层中第2i个极化信道的概率密度函数的均值，
Figure GDA00022655455900000810
表示邻近层中极化信道的概率密度函数的均值。in,
Figure GDA0002265545590000089
is the mean value of the probability density function of the 2ith polarized channel in the decision layer,
Figure GDA00022655455900000810
Represents the mean of the probability density functions of polarized channels in adjacent layers.

递归终止时，其均值为：When the recursion terminates, its mean is:

其中，

Figure GDA00022655455900000812
表示信道层中概率密度函数的均值，σ2表示高斯白噪声的方差。in,
Figure GDA00022655455900000812
represents the mean of the probability density function in the channel layer, and σ2 represents the variance of white Gaussian noise.

根据下式，计算极化子信道的错误概率

Figure GDA00022655455900000813
Calculate the error probability of the polarized sub-channel according to the following formula
Figure GDA00022655455900000813

Figure GDA00022655455900000814
Figure GDA00022655455900000814

其中，

Figure GDA00022655455900000815
表示判决层中第i个极化信道的错误概率，
Figure GDA00022655455900000816
表示判决层中第i个极化信道的均值，Q(x)函数定义如下：in,
Figure GDA00022655455900000815
represents the error probability of the i-th polarized channel in the decision layer,
Figure GDA00022655455900000816
Represents the mean value of the i-th polarized channel in the decision layer, and the Q(x) function is defined as follows:

Figure GDA00022655455900000817
Figure GDA00022655455900000817

对极化子信道的错误概率

Figure GDA00022655455900000818
进行升序排序，选出信息位集Λ；Error probability for polarized subchannels
Figure GDA00022655455900000818
Sort in ascending order, and select the information bit set Λ;

将得到的各极化子信道的错误概率进行升序排序，选出极化信道错误概率最小的k个子信道用于传输比特信息，该集合记为Λ，该集合即是信息位的索引位置，其余子信道用于传输冻结比特，该集合记为Λc，冻结比特集通常传输为全零比特集。Sort the obtained error probability of each polarized sub-channel in ascending order, and select k sub-channels with the smallest polarized channel error probability to transmit bit information. The sub-channel is used to transmit frozen bits, the set is denoted as Λ c , and the frozen bit set is usually transmitted as an all-zero bit set.

步骤3，判断串行消除SC译码序列是否通过循环冗余CRC校验，若是，则执行步骤9，否则，执行步骤4。Step 3, it is judged whether the serial elimination SC decoding sequence passes the CRC check of cyclic redundancy, if yes, go to Step 9, otherwise, go to Step 4.

步骤4，用一个2的整数次方的值初始化串行消除列表算法的列表宽度和比特翻转次数。Step 4, initialize the list width and the number of bit flips of the serial elimination list algorithm with a value of an integer power of 2.

步骤5，选取判决出错的位置集。Step 5, select the location set where the judgment is wrong.

对判决层中信息位所对应的极化信道的对数似然比值绝对值，利用从小到大的次序进行排序，依次选出前T个判决层中极化信道对数似然比值的绝对值所对应的极化信道索引位置，构成串行消除SC译码判决出错位置集，其中T是一个等于比特翻转次数的值。Sort the absolute values of the log-likelihood ratios of the polarized channels corresponding to the information bits in the decision layer in ascending order, and select the absolute values of the log-likelihood ratios of the polarized channels in the first T decision layers in turn. The corresponding polarized channel index position constitutes a serial elimination SC decoding decision error position set, where T is a value equal to the number of bit flips.

步骤6，依次从串行消除SC译码判决出错的位置集中选出一个元素。Step 6: Select one element in turn from the set of positions where the SC decoding judgment error is eliminated in sequence.

步骤7，利用比特翻转串行消除列表算法进行译码。Step 7, decoding using the bit-flip serial elimination list algorithm.

根据当前译码序列的序号是否等于所选出错位置集元素的值分两种情况计算每一个扩展路径的度量值。According to whether the sequence number of the current decoding sequence is equal to the value of the selected error location set element, the metric value of each extension path is calculated in two cases.

情况一：当前译码序列的序号等于所选出错位置集元素的值时，按照下式，使用惩罚因子计算译码树中每一个译码序号等于译码判决出错的位置集中的元素值处的每一个扩展路径的度量值，以间接实现比特翻转。Case 1: When the sequence number of the current decoding sequence is equal to the value of the selected error position set element, use the penalty factor to calculate the value of each decoding sequence in the decoding tree equal to the element value in the error position set in the decoding judgment according to the following formula. The metric value of each extended path to indirectly implement bit flipping.

Figure GDA0002265545590000091
Figure GDA0002265545590000091

其中，

Figure GDA0002265545590000092
表示译码树中由第1位译码比特u1到第i位译码比特ui，所构成的扩展路径的度量值，
Figure GDA0002265545590000093
表示译码树中由第1位译码比特u1到第i-1位译码比特ui-1，所构成的扩展路径的度量值，ue表示串行消除SC译码序列中第e位所对应的比特值，e表示从串行消除SC译码判决出错位置集中选出的元素值，Li表示译码结构判决层中第i位极化信道对数似然比值的绝对值，α表示惩罚因子，其取值范围为100≤α≤2000；in,
Figure GDA0002265545590000092
represents the metric value of the extension path formed by the first decoding bit u 1 to the i-th decoding bit u i in the decoding tree,
Figure GDA0002265545590000093
Represents the metric value of the extension path formed by the first decoding bit u 1 to the i-1 bit decoding bit u i-1 in the decoding tree, and u e represents the e-th decoding sequence in the serial elimination SC decoding sequence. The bit value corresponding to the bit, e represents the element value selected from the set of error positions in the serial elimination SC decoding decision, Li represents the absolute value of the log-likelihood ratio of the i -th polarized channel in the decoding structure decision layer, α represents the penalty factor, and its value range is 100≤α≤2000;

情况二：当前译码序列的序号不等于所选出错位置集元素的值时，按照下式，计算译码树中每一个译码序列的序号处的每一个扩展路径的度量值；Situation 2: When the sequence number of the current decoding sequence is not equal to the value of the selected error position set element, calculate the metric value of each extension path at the sequence number of each decoding sequence in the decoding tree according to the following formula;

Figure GDA0002265545590000094
Figure GDA0002265545590000094

其中，

Figure GDA0002265545590000101
表示译码树中由第1位译码比特u1到第i位译码比特ui，所构成的扩展路径的度量值，表示译码树中由第1位译码比特u1到第i-1位译码比特ui-1，所构成的扩展路径的度量值，∈表示属于操作，Λ表示编码时选出的信息位集，b表示正确的冻结比特值，其值为0，Li表示判决层中第i位极化信道的对数似然比值的绝对值。in,
Figure GDA0002265545590000101
represents the metric value of the extension path formed by the first decoding bit u 1 to the i-th decoding bit u i in the decoding tree, Represents the metric value of the extension path formed by the first decoding bit u 1 to the i-1 bit decoding bit u i-1 in the decoding tree, ∈ indicates that it belongs to the operation, and Λ indicates the information selected during encoding Bit set, b represents the correct frozen bit value, and its value is 0, and Li represents the absolute value of the log-likelihood ratio of the i -th polarized channel in the decision layer.

当扩展路径值是否小于等于串行消除列表算法的列表宽度值，则保留所有扩展路径，否则，对扩展路径的度量值进行从大到小排序，将排序中的前M条扩展路径作为候选路径，其中M取值等于串行消除列表算法的列表宽度值。When the value of the extended path is less than or equal to the list width value of the serial elimination list algorithm, all extended paths are retained; otherwise, the metric values of the extended paths are sorted from large to small, and the first M extended paths in the sorting are used as candidate paths , where M is equal to the list width value of the serial elimination list algorithm.

继续进行以上过程，直至译码进行到译码树中的叶子节点，最终得到候选路径，判断候选路径中是否有通过循环冗余校验的路径，若是，从通过循环冗余检验的候选路径中选取路径度量最大的一条路径作为译码序列后执行步骤9，否则，执行步骤8，其中Q取值等于串行消除列表算法的列表宽度值。Continue the above process until the decoding progresses to the leaf node in the decoding tree, and finally obtain the candidate path, and judge whether there is a path that passes the cyclic redundancy check in the candidate path, and if so, from the candidate path that passes the cyclic redundancy check. After selecting a path with the largest path metric as the decoding sequence, step 9 is performed; otherwise, step 8 is performed, wherein the value of Q is equal to the list width value of the serial elimination list algorithm.

步骤8，判断是否选取完串行消除SC译码判决出错的位置集中的所有元素，若是，则执行步骤10，否则，执行步骤6。Step 8: It is judged whether all elements in the position set where the SC decoding decision is wrong have been selected, if yes, go to Step 10; otherwise, go to Step 6.

步骤9，译码成功，输出译码成功的序列。Step 9: Decoding is successful, and a sequence of successful decoding is output.

步骤10，译码失败，输出串行消除SC译码序列。In step 10, the decoding fails, and the serial-elimination SC decoding sequence is output.

下面结合仿真实验对本发明的效果进一步说明。The effects of the present invention will be further described below in conjunction with simulation experiments.

1.仿真条件：1. Simulation conditions:

本发明的仿真实验是在MATLAB 16.0软件下进行的。在本发明的仿真实验中，为了真实地模拟加性高斯白噪声信道，采用伪随机序列模拟高斯白噪声和使用BPSK对信号进行调制，信源输出端的信息序列采用随机数生成，码率为0.5，码长为1024，极化码的信息位的选取采用高斯近似的方法。The simulation experiment of the present invention is carried out under MATLAB 16.0 software. In the simulation experiment of the present invention, in order to truly simulate the additive white Gaussian noise channel, pseudo-random sequence is used to simulate Gaussian white noise and BPSK is used to modulate the signal, the information sequence at the output end of the signal source is generated by random numbers, and the code rate is 0.5 , the code length is 1024, and the selection of the information bits of the polar code adopts the Gaussian approximation method.

2.仿真内容与结果分析：2. Simulation content and result analysis:

仿真实验1：Simulation Experiment 1:

本发明的仿真实验1是采用本发明的极化码译码方法与三种现有极化码译码方法(串行消除SC方法、循环冗余校验辅助的串行消除列表CRC-SCL方法、基于单比特翻转串行消除SFSC方法)的误帧率对比实验。The simulation experiment 1 of the present invention adopts the polar code decoding method of the present invention and three existing polar code decoding methods (serial elimination SC method, cyclic redundancy check assisted serial elimination list CRC-SCL method) , frame error rate comparison experiment based on single-bit flip serial elimination SFSC method).

图2是本发明的极化码译码方法与三种现有的极化码译码方法(串行消除SC算法、循环冗余校验辅助的串行消除列表CRC-SCL算法、基于单比特翻转串行消除SFSC算法)的误帧率曲线对比图。图2中的横轴表示信噪比，纵轴表示误帧率。图2中以空心圆标示的曲线表示采用现有的串行消除译码算法的极化码译码方法的误帧率曲线。图2中以正方形标示的曲线表示，采用现有技术的基于单比特翻转串行消除SFSC算法，且翻转次数等于4的极化码译码方法的误帧率曲线。图2中以菱形标示的曲线表示采用现有技术的基于单比特翻转串行消除SFSC算法，且翻转次数等于8的极化码译码方法的误帧率曲线。图2中以三角形标示的曲线表示采用现有技术的循环冗余校验辅助的串行消除列表CRC-SCL算法，且列表宽度等于2的极化码译码方法的误帧率曲线。图2中以五角星标示的曲线表示采用本发明的方法，且列表宽度等于2、翻转次数等于4的极化码译码方法的误帧率曲线。图2中以星号标示的曲线表示采用本发明的方法，且列表宽度等于2、翻转次数等于8的极化码译码方法的误帧率曲线。Fig. 2 is the polar code decoding method of the present invention and three existing polar code decoding methods (serial elimination SC algorithm, cyclic redundancy check assisted serial elimination list CRC-SCL algorithm, single-bit based The frame error rate curve comparison chart of flip serial elimination SFSC algorithm). The horizontal axis in FIG. 2 represents the signal-to-noise ratio, and the vertical axis represents the frame error rate. The curve marked with an open circle in FIG. 2 represents the frame error rate curve of the polar code decoding method using the existing serial cancellation decoding algorithm. The curve marked with a square in FIG. 2 represents the frame error rate curve of the polar code decoding method using the prior art based on the single-bit inversion serial elimination SFSC algorithm and the inversion number is equal to 4. The curve marked with a diamond in FIG. 2 represents the frame error rate curve of the polar code decoding method using the prior art based on the single-bit inversion serial elimination SFSC algorithm, and the inversion number is equal to 8. The curve marked with a triangle in FIG. 2 represents the frame error rate curve of the polar code decoding method using the CRC-SCL algorithm assisted by the cyclic redundancy check of the prior art, and the list width is equal to 2. The curve marked with a five-pointed star in FIG. 2 represents the frame error rate curve of the polar code decoding method using the method of the present invention, and the list width is equal to 2 and the number of inversions is equal to 4. The curve marked with an asterisk in FIG. 2 represents the frame error rate curve of the polar code decoding method using the method of the present invention, and the list width is equal to 2 and the number of inversions is equal to 8.

从图2中的星形曲线与菱形曲线、三角形曲线对比可知，在信噪比相等的情况下，星形曲线的误帧率低于菱形曲线和三角形曲线的误帧率，可见，本发明的译码方法相比于基于单比特翻转串行消除译码算法和循环冗余校验辅助的串行消除列表算法的译码方法在性能上都有很大的提升。It can be seen from the comparison between the star-shaped curve, the diamond-shaped curve and the triangular curve in Fig. 2 that, under the condition of equal signal-to-noise ratio, the frame error rate of the star-shaped curve is lower than the frame error rate of the diamond-shaped curve and the triangular curve. Compared with the decoding method based on the single-bit flip serial elimination decoding algorithm and the cyclic redundancy check-assisted serial elimination list algorithm, the decoding method has a great improvement in performance.

仿真实验2：Simulation experiment 2:

本发明的仿真实验2是采用本发明的极化码译码方法与三种现有极化码译码方法(串行消除SC方法、循环冗余校验辅助的串行消除列表CRC-SCL方法、基于单比特翻转串行消除SFSC方法)的归一化的平均复杂度对比实验。The simulation experiment 2 of the present invention adopts the polar code decoding method of the present invention and three existing polar code decoding methods (serial elimination SC method, cyclic redundancy check assisted serial elimination list CRC-SCL method) , based on the single-bit flip serial elimination (SFSC method) of the normalized average complexity comparison experiment.

图3是本发明的极化码译码方法与三种现有的极化码译码方法(串行消除SC算法、循环冗余校验辅助的串行消除列表CRC-SCL算法、基于单比特翻转串行消除SFSC算法)的归一化的平均复杂度对比图。图3中的横轴表示信噪比，纵轴表示归一化的平均译码复杂度，图3中以空心圆标示的曲线表示采用现有技术的串行消除方法的极化码方法的归一化的平均译码复杂度曲线。图3中以正方形标示的曲线表示采用现有技术的基于单比特翻转串行消除SFSC译码算法，且翻转次数等于4的极化码译码方法的归一化的平均译码复杂度曲线。图3中以菱形标示的曲线表示采用现有技术的基于单比特翻转串行消除SFSC译码算法，且翻转次数等于8的极化码译码方法的归一化的平均译码复杂度曲线。图3中以三角形标示的曲线表示采用现有技术的循环冗余校验辅助的串行消除列表CRC-SCL算法，且列表宽度等于2的极化码译码方法的归一化的平均译码复杂度曲线。图3中以五角星标示的曲线表示采用本发明的方法，且列表宽度等于2、翻转次数等于4的极化码译码方法的归一化的平均译码复杂度曲线。图3中以星号标示的曲线表示采用本发明的方法，且列表宽度等于2、翻转次数等于8的极化码译码方法的归一化的平均译码复杂度曲线。Fig. 3 is the polar code decoding method of the present invention and three existing polar code decoding methods (serial elimination SC algorithm, cyclic redundancy check assisted serial elimination list CRC-SCL algorithm, single-bit based Comparison plot of normalized average complexity of flipped serial elimination (SFSC algorithm). The horizontal axis in FIG. 3 represents the signal-to-noise ratio, the vertical axis represents the normalized average decoding complexity, and the curve marked with an open circle in FIG. 3 represents the normalization of the polar coding method using the serial cancellation method in the prior art Normalized average decoding complexity curve. The curve marked with a square in FIG. 3 represents the normalized average decoding complexity curve of the polar code decoding method using the prior art based on single-bit inversion serial elimination SFSC decoding algorithm and the inversion number is equal to 4. The curve marked with diamonds in FIG. 3 represents the normalized average decoding complexity curve of the polar code decoding method using the prior art based on single-bit inversion serial elimination SFSC decoding, and the inversion number is equal to 8. The curve marked with a triangle in FIG. 3 represents the normalized average decoding of the polar code decoding method using the prior art CRC-SCL assisted serial elimination list algorithm and the list width is equal to 2 complexity curve. The curve marked with a five-pointed star in FIG. 3 represents the normalized average decoding complexity curve of the polar code decoding method using the method of the present invention, and the list width is equal to 2 and the number of inversions is equal to 4. The curve marked with an asterisk in FIG. 3 represents the normalized average decoding complexity curve of the polar code decoding method using the method of the present invention, and the list width is equal to 2 and the number of inversions is equal to 8.

从图3中的星形曲线与圆形曲线对比可知，在高信噪比情况下，星形曲线逐渐与菱形曲线重叠，因此本发明改进的方法，随着信噪比的提升，译码方法的复杂度逐渐趋近于串行消除SC的译码的复杂度，译码复杂度明显降低。It can be seen from the comparison between the star-shaped curve and the circular curve in Fig. 3 that in the case of high signal-to-noise ratio, the star-shaped curve gradually overlaps with the diamond-shaped curve. Therefore, in the improved method of the present invention, with the improvement of the signal-to-noise ratio, the decoding method The complexity gradually approaches the decoding complexity of serial elimination SC, and the decoding complexity is obviously reduced.

Claims (3)

1, polar code decoding method based on bit reversal serial elimination list algorithm, characterized in that, the concrete steps include the following:
(1) receiving a sequence to be decoded from a communication terminal:
(2) performing serial elimination SC decoding on a sequence to be decoded:
(2a) calculating the log-likelihood ratio of the polarized channel;
(2b) judging the sequence received by the communication terminal according to the positive and negative of the log-likelihood ratio of each polarized channels corresponding to the information bits in the decoding structure judgment layer, if the sequence is positive, judging the sequence to be 0, if the sequence is negative, judging the sequence to be 1, and directly judging the position bits corresponding to each non-information bits in the sequence received by the communication terminal to be 0;
(2c) judging whether the serial number of the current decoding sequence is larger than the code length of the polarization code, if so, executing the step (3) after taking the current decoding sequence as a serial elimination SC decoding sequence, otherwise, executing the step (2a) after adding 1 to the serial number of the current decoding sequence;
(3) judging whether the serial elimination SC decoding sequence passes through cyclic redundancy CRC (cyclic redundancy check), if so, executing the step (9), otherwise, executing the step (4):
(4) initializing the list width and the bit flipping times of the serial elimination list algorithm by using values of 2 to the power of an integer;
(5) selecting a position set with a wrong judgment:
according to a sorting method from small to large, sequentially selecting the positions with decoding judgment errors corresponding to the information bit set from a serial elimination SC decoding sequence which does not pass through cyclic redundancy CRC (cyclic redundancy check), and forming the positions with errors into a position set with serial elimination SC decoding judgment errors;
(6) elements are selected from a position set for serially eliminating SC decoding judgment errors in sequence;
(7) decoding by using a bit flipping serial elimination list algorithm:
(7a) judging whether the sequence number of the current decoding sequence is equal to the value of the selected error position set element, if so, executing the step (7b), otherwise, executing the step (7 c);
(7b) calculating the metric value of each expansion paths at the position where each decoding sequence numbers in the decoding tree are equal to the element value in the position set with the decoding judgment error by using a penalty factor according to the following formula so as to indirectly realize bit flipping;
Figure FDA0002265545580000011
wherein,
Figure FDA0002265545580000021
indicating the bit u decoded by bit 1 in the decoding tree1Decoding bit u to ith bitiThe values of the metrics of the constructed extension paths,
Figure FDA0002265545580000022
indicating the bit u decoded by bit 1 in the decoding tree1Decoding bit u to i-1 biti-1Metric values of the formed extension paths, ueIndicating the bit value corresponding to the e-th bit in the serial elimination SC decoding sequence, e indicating the value of an element selected from the set of serial elimination SC decoding decision error positions, LiRepresenting the absolute value of the log-likelihood ratio of the ith polarization channel in the decision layer of the decoding structure, and α representing a penalty factor, wherein the value range of the penalty factor is more than or equal to 100 and less than or equal to α and less than or equal to 2000;
(7c) calculating the metric value of each expansion paths at the sequence number of each decoding sequences in the decoding tree according to the following formula;
wherein,
Figure FDA0002265545580000024
indicating the bit u decoded by bit 1 in the decoding tree1Decoding bit u to ith bitiThe values of the metrics of the constructed extension paths,
Figure FDA0002265545580000025
indicating the bit u decoded by bit 1 in the decoding tree1Decoding bit u to i-1 biti-1The metric value of the formed extended path belongs to operation, wherein the epsilon represents the selected information bit set during coding, the lambda represents the correct frozen bit value, the value of which is 0, and the value of LiRepresenting the absolute value of the log-likelihood ratio of the ith bit polarization channel in the decision layer;
(7d) judging whether the metric value of the extended path is less than or equal to the list width value of the serial elimination list algorithm, if so, executing the step (7e), otherwise, executing the step (7 f);
(7e) reserving all the extension paths;
(7f) sorting the metric values of the extended paths from large to small, and taking the first Q extended paths in the sorting as candidate paths, wherein the value of Q is equal to the list width value of a serial elimination list algorithm;
(7g) judging whether the serial number of the current decoding sequence is larger than the code length of the polarization code, if so, executing the step (7h), otherwise, adding 1 to the serial number of the current decoding sequence and executing the step (7 a);
(7h) judging whether the candidate paths have paths passing the cyclic redundancy check, if so, selecting paths with the maximum path metric from the candidate paths passing the cyclic redundancy check as a decoding sequence, and then executing the step (9), otherwise, executing the step (8);
(8) judging whether all elements in the position set with errors in serial elimination SC decoding judgment are selected, if so, executing the step (10), otherwise, executing the step (6);
(9) decoding is successful, and a successfully decoded sequence is output;
(10) if the decoding fails, the serial cancellation SC decoding sequence is output.
2. The method for decoding polar codes based on the bit flipping senium elimination list algorithm according to claim 1, wherein the calculating the log-likelihood ratio of the polarized channel in step (2a) is to calculate the log-likelihood ratio of the polarized channel in the decision layer of the decoding structure according to the parity of the serial number of the polarized channel:
A. calculating the log-likelihood ratio of each polarized channel with odd serial number in the decision layer of the decoding structure according to the following formula;
wherein,
Figure FDA0002265545580000032
the input of the polarization channel of the kth odd-numbered sequence number in the decoding structure decision layer which represents the length of the polarization code word is N is
Figure FDA0002265545580000033
K represents the serial number of the polarized channel in the decision layer of the decoding structure, the value of the serial number is 2j-1, j is more than or equal to 1 and less than or equal to N/2, N represents the code word length after the code coding of the polarized code,representing the input of the polarized channel, y represents the sequence received by the communication terminal,
Figure FDA0002265545580000035
represents the decoded first k-1 bit code word sequence, sign (h) represents code words1And L2When the product of (A) is positive, the function value is 1, and when L is positive1And L2When the product of (a) is negative, the function value is a function of-1, L1Representing the log-likelihood ratio, L, of the polarized channel of the upper branch in the adjacent layers of the decoding structure2Represents the log-likelihood ratio of the polarized channel of the lower branch in the adjacent layer of the decoding structure, min (-) represents the function of solving the minimum value of two real numbers, | - | represents the operation of solving the absolute value:
B. calculating the log-likelihood ratio of each polarized channel with even serial number in the decision layer of the decoding structure according to the following formula;
Figure FDA0002265545580000036
wherein,the input of the polarization channel of the mth even serial number in the decoding structure decision layer which represents the length of the polarization code word as N is
Figure FDA0002265545580000038
M represents the serial number of the polarized channel in the decision layer of the decoding structure, the value of the serial number is 2j, j is more than or equal to 1 and less than or equal to N/2, N represents the code word length after the polarized code is coded,
Figure FDA0002265545580000041
representing the input of the polarized channel, y represents the sequence received by the communication terminal,
Figure FDA0002265545580000042
representing the first m-1 bit codeword sequence that has been decoded,
Figure FDA0002265545580000043
indicating the m-1 th bit of the codeword, L, that has been decoded1Representing the log-likelihood ratio, L, of the polarized channel of the upper branch in the adjacent layers of the decoding structure2Representing the log-likelihood ratio of the polarized channel of the lower branch in the layer adjacent to the decoding structure.
3. The polar code decoding method based on the bit flipping serial elimination list algorithm according to claim 1, wherein the sorting method from small to large in step (5) specifically comprises sorting log likelihood ratio absolute values of polar channels corresponding to information bits in a decision layer from small to large, sequentially selecting polar channel index positions corresponding to absolute values of log likelihood ratios of first T polar channels to form a decision error position set, wherein T is values equal to the number of bit flipping times.
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