Low Complexity Successive Cancellation List Decoding of U-UV Codes

Constituted by BCH component codes and its ordered statistics decoding(OSD),the successive cancellation list(SCL)decoding of U-UV structural codes can provide competent error-correction performance in the short-to-medium length regime.However,this list decoding complexity becomes formidable as the decoding output list size increases.This is primarily incurred by the OSD.Addressing this challenge,this paper proposes the low complexity SCL decoding through reducing the complexity of component code decoding,and pruning the redundant SCL decoding paths.For the former,an efficient skipping rule is introduced for the OSD so that the higher order decoding can be skipped when they are not possible to provide a more likely codeword candidate.It is further extended to the OSD variant,the box-andmatch algorithm(BMA),in facilitating the component code decoding.Moreover,through estimating the correlation distance lower bounds(CDLBs)of the component code decoding outputs,a path pruning(PP)-SCL decoding is proposed to further facilitate the decoding of U-UV codes.In particular,its integration with the improved OSD and BMA is discussed.Simulation results show that significant complexity reduction can be achieved.Consequently,the U-UV codes can outperform the cyclic redundancy check(CRC)-polar codes with a similar decoding complexity.

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.

List-Serial Pipelined Hardware Architecture for SCL Decoding of Polar Codes

For polar codes,the performance of successive cancellation list(SCL)decoding is capable of approaching that of maximum likelihood decoding.However,the existing hardware architectures for the SCL decoding suffer from high hardware complexity due to calculating L decoding paths simultaneously,which are unfriendly to the devices with limited logical resources,such as field programmable gate arrays(FPGAs).In this paper,we propose a list-serial pipelined hardware architecture with low complexity for the SCL decoding,where the serial calculation and the pipelined operation are elegantly combined to strike a balance between the complexity and the latency.Moreover,we employ only one successive cancellation(SC)decoder core without L×L crossbars,and reduce the number of inputs of the metric sorter from 2L to L+2.Finally,the FPGA implementations show that the hardware resource consumption is significantly reduced with negligible decoding performance loss.

一种自适应快速SSCL极化码译码算法

极化码的简化串行抵消列表(Simplified Successive Cancellation List,SSCL)译码提出了R1(Rate-1)、R0(Rate-0)等多种特殊节点的快速译码算法,一定程度改善了SCL译码复杂度高和时延大的问题,但当节点信息比特数量较大时仍存在大量的冗余计算。针对R1等信息比特较多的节点,提出了一种基于路径度量(Path Metric,PM)的自适应路径选择策略,无需先验信息设置阈值,在不降低SSCL译码性能的条件下能有效降低排序复杂度,减少所需时间步数,提升Polar码译码效率。仿真和实验结果表明,在保证纠错性能的前提下,该算法针对R1节点译码所需的时间步数相对传统SCL译码降低了约83%,相对SSCL降低了约47%,相对快速SSCL降低了约18%。同时,相对基于搜索集和决策函数的SCL译码算法译码效率也有较大提高,其所需时间步数受码字结构及信道环境自适应改变,但不大于快速SSCL译码算法所需时间步数。

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.

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.

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。

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。

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。

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。

分段CRC辅助极化码SCL比特翻转译码算法

极化码是一种被严格证明到达信道容量的信道编码方法。虽然串行抵消列表比特翻转(SCLF)译码算法可提高译码性能,但导致较高的译码复杂度。为降低译码复杂度,提出一种分段CRC辅助串行抵消列表比特翻转极化码译码算法。该算法在码字构造过程中,通过添加分段CRC校验,可提前终止翻转译码过程。在中短码长下,可显著降低极化码比特翻转译码复杂度。仿真结果表明,当L=8,Eb N0=1.5 dB时,与SCLF方法翻转2 bit译码算法相比,提出方法的译码复杂度可降低71.9%,同时获得较好的性能增益。

“太极混一”——极化码原理及5G应用

极化码是第一种达到信道容量的构造性编码,已列入5G移动通信的控制信道编码标准,这是信道编码领域近年来的重大突破。旨在阐述极化码的基本原理与5G中的应用。基于信道极化观点,分析了极化码蝶形编码结构与基本的串行抵消译码算法,提出了级联极化编码结构,并归纳了高性能译码算法的特点。另外,还深入分析了5G移动通信中极化码设计的基本思想,概括了极化码实用编码的3种方式:凿孔、缩短与重复。最后,指出极化信息处理是未来通信系统优化的新型方法。

极化码串行抵消译码算法的改进设计

极化码是首次以构造性方法逼近信道容量的码。尽管编码和译码都具有较低的复杂度，但在中短码长时，性能并不理想，对此提出了一种采用CRC作为内码并与极化码级联的方案，与现有方案不同的是在译码时仅对内码位之间的位采用列表译，从而获得较低的译码复杂度。从仿真结果看，该算法在BEC信道下显著提高极化码的性能，并接近最大似然译码的性能，在AWGN信道下可获得0．5db的性能改善。

极化码列表译码算法优化分析

极化码目前是5G通信技术中的信道编码之一。串行抵消列表译码算法是极化码中最受欢迎的译码算法之一。尽管现有的列表译码算法已经得到优化,但是算法中存在数据相同且未被更新的存储空间,造成存储空间的不必要开销,也增加了计算量。论文在原有算法的基础上对算法进行优化,有效节省存储空间,仿真表明,计算量也得到一定的降低。

极化码串行抵消译码算法的改进设计

极化码是基于信道极化(Channel Polarization)现象,首次以构造性的方法逼近信道容量的码。尽管极化码的编码和译码都具有较低的复杂度,但在中短码长时,极化码的性能并不理想,甚至不如LDPC和Turbo码。针对这一问题,提出了一种采用CRC作为内码,并与极化码级联的方案。与现有方案不同的是算法在译码时仅对内码位之间的位采用列表译,从而获得较低的译码复杂度。从仿真结果看,算法在BEC信道下可以显著地提高极化码的性能,并接近最大似然译码的性能;在AWGN信道下可以获得0.5dB的性能改善。

一种低时延极化码列表连续删除译码算法

为进一步降低译码时延,提出一种基于路径复用的低时延自适应列表连续删除译码算法。针对不同列表连续删除译码间存在重复路径的现象,采用基于CRC校验的重复路径复用的译码方案。仿真结果表明,与传统CA-SCL算法以及AD-SCL算法相比,该译码算法能够在信噪比较低的信道中保持较高的译码性能,并获得更低的译码时延。