Improved Polar Decoder Utilizing Neural Network in Fast Simplified Successive-Cancellation Decoding

Polar codes using successive-cancellation decoding always suffer from high latency for its serial nature. Fast simplified successive-cancellation decoding algorithm improves the situation in theoretically but not performs well as expected in practical for the workload of nodes identification and the existence of many short blocks. Meanwhile, Neural network (NN) based decoders have appeared as potential candidates to replace conventional decoders for polar codes. But the exponentially increasing training complexity with information bits is unacceptable which means it is only suitable for short codes. In this paper, we present an improvement that increases decoding efficiency without degrading the error-correction performance. The long polar codes are divided into several sub-blocks, some of which can be decoded adopting fast maximum likelihood decoding method and the remained parts are replaced by several short codes NN decoders. The result shows that time steps the proposed algorithm need only equal to 79.8% of fast simplified successive-cancellation decoders require. Moreover, it has up to 21.2 times faster than successive-cancellation decoding algorithm. More importantly, the proposed algorithm decreases the hardness when applying in some degree.

RETRACTED: <i>Improved Polar Decoder Utilizing Neural Network in Fast Simplified Successive-Cancellation Decoding</i>

This article has been retracted to straighten the academic record. In making this decision the Editorial Board follows COPE's Retraction Guidelines. The aim is to promote the circulation of scientific research by offering an ideal research publication platform with due consideration of internationally accepted standards on publication ethics. The Editorial Board would like to extend its sincere apologies for any inconvenience this retraction may have caused. Please see the article page for more details. The full retraction notice in PDF is preceding the original paper which is marked "RETRACTED".

A simplified decoding algorithm for multi-CRC polar codes

Polar codes represent one of the major breakthroughs in 5G standard,and have been proven to be able to achieve the symmetric capacity of binary-input discrete memoryless channels using the successive cancellation list(SCL)decoding algorithm.However,the SCL algorithm suffers from a large amount of memory overhead.This paper proposes an adaptive simplified decoding algorithm for multiple cyclic redundancy check(CRC)polar codes.Simulation results show that the proposed method can reduce the decoding complexity and memory space.It can also acquire the performance gain in the low signal to noise ratio region.

Deep Learning Aided SCL Decoding of Polar Codes with Shifted-Pruning

Recently,a generalized successive cancellation list(SCL)decoder implemented with shiftedpruning(SP)scheme,namely the SCL-SP-ωdecoder,is presented for polar codes,which is able to shift the pruning window at mostωtimes during each SCL re-decoding attempt to prevent the correct path from being eliminated.The candidate positions for applying the SP scheme are selected by a shifting metric based on the probability that the elimination occurs.However,the number of exponential/logarithm operations involved in the SCL-SP-ωdecoder grows linearly with the number of information bits and list size,which leads to high computational complexity.In this paper,we present a detailed analysis of the SCL-SP-ωdecoder in terms of the decoding performance and complexity,which unveils that the choice of the shifting metric is essential for improving the decoding performance and reducing the re-decoding attempts simultaneously.Then,we introduce a simplified metric derived from the path metric(PM)domain,and a custom-tailored deep learning(DL)network is further designed to enhance the efficiency of the proposed simplified metric.The proposed metrics are both free of transcendental functions and hence,are more hardware-friendly than the existing metrics.Simulation results show that the proposed DL-aided metric provides the best error correction performance as comparison with the state of the art.

Quantized Decoders that Maximize Mutual Information for Polar Codes

In this paper,we innovatively associate the mutual information with the frame error rate(FER)performance and propose novel quantized decoders for polar codes.Based on the optimal quantizer of binary-input discrete memoryless channels(BDMCs),the proposed decoders quantize the virtual subchannels of polar codes to maximize mutual information(MMI)between source bits and quantized symbols.The nested structure of polar codes ensures that the MMI quantization can be implemented stage by stage.Simulation results show that the proposed MMI decoders with 4 quantization bits outperform the existing nonuniform quantized decoders that minimize mean-squared error(MMSE)with 4 quantization bits,and yield even better performance than uniform MMI quantized decoders with 5 quantization bits.Furthermore,the proposed 5-bit quantized MMI decoders approach the floating-point decoders with negligible performance loss.

Multiple CRC-aided variable successive cancellation list decoder of polar codes

In order to change the path candidates, reduce the average list size, and make more paths pass cyclic redundancy check （CRC）, multiple CRC-aided variable successive cancellation list （SCL） decoding algorithm is proposed. In the decoding algorithm, the whole unfrozen bits are divided into several parts and each part is concatenated with a corresponding CRC code, except the last part which is concatenated with a whole unfrozen CRC code. Each CRC detection is performed, and only those satisfying each part CRC become the path candidates. A variable list is setup for each part to reduce the time complexity. Variable list size is setup for each part to reduce the time complexity until one survival path in each part can pass its corresponding CRC. The results show that the proposed algorithm can reduce the average list size, and the frame error rate （FER） performance, and has a better performance with the increase of the part number.

Polar Codes多比特同时判定高输出SC算法研究

polar codes具有丰富的代数结构和优秀的分析特性,具有明确的编码方法和译码算法,但是其连续删除译码算法由于采用串行按位译码的方法,从而导致整体译码时间较长。利用改进的路径度量值计算方法减少了SC译码器判定的次数,从而使得整体的译码时间大大降低,提高了原SC算法测输出。实验数据表明该方法不仅拥有较低的译码时间,同时还能获得更好的性能。

A Golden Decade of Polar Codes:From Basic Principle to 5G Applications

After the pursuit of seventy years,the invention of polar codes indicates that we have found the first capacity-achieving coding with low complexity construction and decoding,which is the great breakthrough of the coding theory in the past two decades.In this survey,we retrospect the history of polar codes and summarize the advancement in the past ten years.First,the primary principle of channel polarization is investigated such that the basic construction,coding method and the classic successive cancellation(SC)decoding are reviewed.Second,in order to improve the performance of the finite code length,we introduce the guiding principle and conclude five design criteria for the construction,design and implementation of the polar code in the practical communication system based on the exemplar schemes in the literature.Especially,we explain the design principle behind the concatenated coding and rate matching of polar codes in 5G wireless system.Furthermore,the improved SC decoding algorithms,such as SC list(SCL)decoding and SC stack(SCS)decoding etc.,are investigated and compared.Finally,the research prospects of polar codes for the future 6G communication system are explored,including the optimization of short polar codes,coding construction in fading channels,polar coded modulation and HARQ,and the polar coded transmission,namely polar processing.Predictably,as a new coding methodology,polar codes will shine a light on communication theory and unveil a revolution in transmission technology.

动态扰动辅助的串行抵消双比特翻转Polar译码算法

针对串行抵消翻转译码算法(Successive Cancellation Flip,SCF)受限于单比特翻转而性能提升有限问题,提出了一种双比特翻转译码算法(Successive Cancellation Flip with 2 Bits,SCF2)。针对SCP算法扰动方差初始值固定的问题,设计了一种扰动方差可随码长和码率变化的改进SCP算法。在此基础上,结合翻转和扰动机制,提出了一种动态扰动辅助的串行抵消双比特翻转(Dynamic Perturbation-Aided SCF2,DPA-SCF2)译码算法,并对其译码复杂度和性能进行了分析。仿真结果显示,相比于列表长度为4的循环冗余校验辅助串行抵消列表(Cyclic Redundancy Check Aided Successive Cancellation List,CA-SCL)译码算法,所提算法最大可获得约0.5 dB的性能增益。

基于单调排序与并行选择的连续删除堆栈译码器的硬件实现

极化码得益于其较低的复杂度和灵活的构造,成为了当今最为流行的信道编码方式。然而,与其他信道编码的译码算法相比,极化码中的连续删除(Successive Cancellation, SC)译码算法的性能较差。为了解决这一问题,连续删除列表(Successive Cancellation List, SCL)、连续删除堆栈(Successive Cancellation Stack, SCS)等基于连续删除译码的改进算法问世,并显著地改善了其纠错性能。其中,连续删除堆栈译码算法是以更高的复杂度为代价的,特别是在路径选择过程中。本文提出了一种新型的路径选择硬件架构,该架构通过对路径信息分组存储,用分组单调排序与并行比较相结合的策略进行最优路径选择,降低了硬件资源消耗的同时提高了路径选择的硬件效率。最后在现场可编程门阵列(Field Programmable Gate Array, FPGA)上实现了该架构,硬件实现结果验证了本文提出的架构与现有的SCS译码器拥有相近的纠错性能的同时,整体资源开销在查找表(Look Up Table, LUT)、寄存器(Register)和块随机存储器(Block Random Access Memory, BRAM)上分别减少了24.06%,56.42%和39.29%,吞吐率提高了24.38%。

极化码的Reed-Solomon内核软判决译码

极化码的极化速率与译码复杂度取决于其采用的内核。本文考虑了具有Reed-Solomon内核的极化码的有效软判决译码问题,提出了一种基于分圆FFT算法的内核分解,结合逐次抵消译码算法能够实现对数似然比的近似最佳评估,并且降低了译码复杂度。数值仿真结果表明,利用Reed-Solomon内核的极化码的软判决译码的帧错误率性能优于传统的Arikan内核的极化码。

极化码的分布式CRC辅助低复杂度逐次抵消翻转译码

为提高极化码的译码效率,文中提出了一种新颖的逐次抵消翻转(SCF)译码。与传统的SCF译码相比,其可以使用分布式CRC比特来降低计算复杂度。该译码通过提前终止对第一次SC译码的失败帧的译码,来减少信息比特的估计数量,同时尝试最小化附加的排序操作。仿真结果表明,与传统的SCF译码相比,该SCF译码将重复SC译码的计算复杂度至少降低了27%。

极化码与奇偶校验码的级联编码:面向5G及未来移动通信的编码方案

基于信道极化定理而提出的极化码是目前唯一被严格理论证明可以达到香农容量限的编码,并被接受为第五代移动通信系统(5G)中短码控制信道的编码方案。本文首先给出极化码的编码和译码原理,然后提出一种极化码与奇偶校验码级联的设计方案,发送端编码器采用奇偶校验码作为外码,极化码作为内码的级联编码结构。接收端译码器采用基于奇偶校验辅助的连续消除列表译码算法。相比于极化码与循环冗余校验码的级联方案,本文提出的级联设计方案具有更加优良的纠错性能,且没有提升编、译码的复杂度,有能力满足5G移动通信控制信道对纠错性能的要求。

低时间复杂度的极化码译码算法

极化码的串行抵消列表(successive cancellation list,SCL)译码算法是目前应用最广泛的译码算法,但是复杂度和时延很高。为了降低时间复杂度,提出了一种基于综合检测(syndrome check,SC)的快速SCL译码与球形列表(list sphere decoding,LSD)译码相联合的办法,简称SC-SCSL(syndrome check successive cancellation sphere list)译码。该算法避免了SCL译码在不同路径的相同节点同时满足综合检测时,极易导致结果出错的情况,仿真结果表明,在同时满足综合检测时性能与SCL相差不大;同时联合了LSD译码,来降低时间复杂度。在几乎不损失性能的情况下,相比于循环冗余协助下的串行抵消列表(cyclic redundancy check aided successive cancellation list,CA-SCL)译码降低了50%~55%的时间复杂度。

极化码自适应连续消除列表比特翻转译码算法

极化码是一种新型的信道编码方法,并且具有较低的译码复杂度,第三代合作伙伴计划(3rd generation partnership project,3GPP)组织已经确定将极化码作为5G通信中增强移动宽带场景下的信道编码方案,目前极化码译码已经成为编码领域备受瞩目的研究热点。极化码连续消除列表比特翻转(successive cancellation list flip,SCLF)译码算法通过翻转不可靠的比特进行额外的SCL译码尝试来提高SCL译码性能。但SCLF译码算法为了提高译码性能而设置较大的路径保留数,导致译码复杂度偏高。通过动态选择路径保留数,提出了一种自适应连续消除列表比特翻转(adaptive-SCLF)AD-SCLF译码算法,该算法从较小的路径保留数(L=1)开始译码,并迭代地增加路径保留数,直到至少有一条路径通过循环冗余校验(cyclic redundancy check,CRC)校验,保证在译码性能不变的情况下降低译码复杂度。仿真结果表明,在加性高斯白噪声(additive white Gaussian noise,AWGN)信道和Rayleigh信道下,与传统SCLF译码算法相比,AD-SCLF算法在中高信噪比下明显降低了复杂度。

基于预译码的极化码最大似然简化连续消除译码算法

针对极化码译码串行输出造成较大译码时延的问题,该文提出一种基于预译码的最大似然简化连续消除译码算法。首先对译码树节点存储的似然值进行符号提取并分组处理,得到符号向量组;然后比较符号向量组与该节点的某些信息位的取值情况,发现向量组中储存的正负符号分布规律与该节点的中间信息位的取值具有一一对应的关系;在此基础上对组合码中间的1～2 bit进行预译码;最后结合最大似然译码方法估计组合码中的剩余信息位,从而得到最终的译码结果。仿真结果表明:在不影响误码性能的情况下,所提算法与已有的算法相比可有效降低译码时延。

一种基于整数操作的极化码最小和译码算法

通过信道极化,极化码理论上证明可渐进达到香农限。文中研究极化码在高斯信道下的串行抵消(successive cancellation,SC)译码算法,提出了一种基于整数操作的最小和译码算法。算法中信道输出值被均匀量化后再取整数,作为SC译码器的输入;节点更新使用最小和算法,更新过程不需要量化操作,直接使用信道输出值量化后的整数值。数值仿真结果表明,在信噪比小于4 d B时,译码性能与基于浮点运算的原始SC译码一致;当误比特率为10-5时,提出的算法与原始SC译码的信噪比相差0.2 d B。所提出的算法便于硬件实现,运算中变量的大小都用8比特整数表示。

一种极化码联合SC球形列表译码算法

为了降低极化码译码复杂度,提出了一种极化码联合SC球形列表(joint successive cancellation sphere list,JSCSL)译码算法。JSCSL译码算法结合了串行消除列表(successive cancellation list,SCL)译码和球形列表(list sphere decoding,LSD)译码相同的列表结构,联合不同的译码流程,增加译码并行性,从而降低译码复杂度。JSCSL译码算法将码字分割,在2个方向上使用不同译码方案,即从前往后和从后往前分别采取SCL译码和LSD译码,最终选取满足冗余循环校验(cyclic redundancy check,CRC)校验的码字。理论推导了2部分译码的中间分割点,使得独立译码时间近似,以达到最优的并行译码。仿真结果表明,与性能较优的CA-SCL(CRC-aided successive cancellation list)译码算法相比,JSCSL译码算法性能与其相近,但译码复杂度降低了40%~50%,因此,JSCSL译码算法在译码性能和复杂度达到新的平衡。

基于CNN扰动的极化码译码算法

针对中短码长下串行抵消(SC)算法性能较差,且串行抵消列表(SCL)算法复杂度较高等问题,根据译码纠错空间理论,该文提出了一种基于卷积神经网络(CNN)扰动的极化码译码算法。对SC译码失败的接收序列,通过CNN产生相应的扰动噪声,并将该扰动噪声添加到接收信号中,然后根据重新计算的似然信息进行译码。仿真结果表明:与SC译码算法相比,所提出的算法约有0.6 dB的增益,与SCL(L=16)译码算法相比,该算法约有0.1 dB的提升,且平均复杂度更低。

基于分段循环冗余校验的极化码自适应连续取消列表译码算法

针对极化码连续取消列表(SCL)译码算法为获取较好性能而采用较多的保留路径数,导致译码复杂度较高的缺点,自适应SCL译码算法虽然在高信噪比下降低了一定的计算量,却带来了较高的译码延时。根据极化码的顺序译码结构,该文提出了一种分段循环冗余校验(CRC)与自适应选择保留路径数量相结合的SCL译码算法。仿真结果表明,与传统CRC辅助SCL译码算法、自适应SCL译码算法相比,该算法在码率R=0.5时,低信噪比下(-1dB)复杂度降低了约21.6%,在高信噪比下(3dB)复杂度降低了约64%,同时获得较好的译码性能。