Improved Segmented Belief Propagation List Decoding for Polar Codes with Bit-Flipping

Belief propagation list(BPL) decoding for polar codes has attracted more attention due to its inherent parallel nature. However, a large gap still exists with CRC-aided SCL(CA-SCL) decoding.In this work, an improved segmented belief propagation list decoding based on bit flipping(SBPL-BF) is proposed. On the one hand, the proposed algorithm makes use of the cooperative characteristic in BPL decoding such that the codeword is decoded in different BP decoders. Based on this characteristic, the unreliable bits for flipping could be split into multiple subblocks and could be flipped in different decoders simultaneously. On the other hand, a more flexible and effective processing strategy for the priori information of the unfrozen bits that do not need to be flipped is designed to improve the decoding convergence. In addition, this is the first proposal in BPL decoding which jointly optimizes the bit flipping of the information bits and the code bits. In particular, for bit flipping of the code bits, a H-matrix aided bit-flipping algorithm is designed to enhance the accuracy in identifying erroneous code bits. The simulation results show that the proposed algorithm significantly improves the errorcorrection performance of BPL decoding for medium and long codes. It is more than 0.25 d B better than the state-of-the-art BPL decoding at a block error rate(BLER) of 10^(-5), and outperforms CA-SCL decoding in the low signal-to-noise(SNR) region for(1024, 0.5)polar codes.

Low-loss belief propagation decoder with Tanner graph in quantum error-correction codes

Quantum error-correction codes are immeasurable resources for quantum computing and quantum communication.However,the existing decoders are generally incapable of checking node duplication of belief propagation(BP)on quantum low-density parity check(QLDPC)codes.Based on the probability theory in the machine learning,mathematical statistics and topological structure,a GF(4)(the Galois field is abbreviated as GF)augmented model BP decoder with Tanner graph is designed.The problem of repeated check nodes can be solved by this decoder.In simulation,when the random perturbation strength p=0.0115-0.0116 and number of attempts N=60-70,the highest decoding efficiency of the augmented model BP decoder is obtained,and the low-loss frame error rate(FER)decreases to 7.1975×10^(-5).Hence,we design a novel augmented model decoder to compare the relationship between GF(2)and GF(4)for quantum code[[450,200]]on the depolarization channel.It can be verified that the proposed decoder provides the widely application range,and the decoding performance is better in QLDPC codes.

Distributed Resource Allocation in Ultra-Dense Networks via Belief Propagation

Ultra-dense networking is widely accepted as a promising enabling technology to realize high power and spectrum efficient communications in future 5G communication systems. Although joint resource allocation schemes promise huge performance improvement at the cost of cooperation among base stations,the large numbers of user equipment and base station make jointly optimizing the available resource very challenging and even prohibitive. How to decompose the resource allocation problem is a critical issue. In this paper,we exploit factor graphs to design a distributed resource allocation algorithm for ultra dense networks,which consists of power allocation,subcarrier allocation and cell association. The proposed factor graph based distributed algorithm can decompose the joint optimization problem of resource allocation into a series of low complexity subproblems with much lower dimensionality,and the original optimization problem can be efficiently solved via solving these subproblems iteratively. In addition,based on the proposed algorithm the amounts of exchanging information overhead between the resulting subprob-lems are also reduced. The proposed distributed algorithm can be understood as solving largely dimensional optimization problem in a soft manner,which is much preferred in practical scenarios. Finally,the performance of the proposed low complexity distributed algorithm is evaluated by several numerical results.

VARIABLE NON-UNIFORM QUANTIZED BELIEF PROPAGATION ALGORITHM FOR LDPC DECODING

Non-uniform quantization for messages in Low-Density Parity-Check(LDPC)decoding canreduce implementation complexity and mitigate performance loss.But the distribution of messagesvaries in the iterative decoding.This letter proposes a variable non-uniform quantized Belief Propaga-tion(BP)algorithm.The BP decoding is analyzed by density evolution with Gaussian approximation.Since the probability density of messages can be well approximated by Gaussian distribution,by theunbiased estimation of variance,the distribution of messages can be tracked during the iteration.Thusthe non-uniform quantization scheme can be optimized to minimize the distortion.Simulation resultsshow that the variable non-uniform quantization scheme can achieve better error rate performance andfaster decoding convergence than the conventional non-uniform quantization and uniform quantizationschemes.

Belief Propagation List Decoding for Polar Codes:Performance Analysis and Software Implementation on GPU

Belief propagation(BP)decoding outputs soft information and can be naturally used in iterative receivers.BP list(BPL)decoding provides comparable error-correction performance to the successive cancellation list(SCL)decoding.In this paper,we firstly introduce an enhanced code construction scheme for BPL decoding to improve its errorcorrection capability.Then,a GPU-based BPL decoder with adoption of the new code construction is presented.Finally,the proposed BPL decoder is tested on NVIDIA RTX3070 and GTX1060.Experimental results show that the presented BPL decoder with early termination criterion achieves above 1 Gbps throughput on RTX3070 for the code(1024,512)with 32 lists under good channel conditions.

3×3核矩阵极化码的BP译码算法

相比于2×2核极化码,3×3核极化码的码长更加丰富以及有着更高的极化速率。同时,极化码的置信传播(Belief Propagation, BP)算法相比于传统串行消去(Successive Cancellation, SC)译码算法具有更低的延时。将2×2核极化码的BP译码算法推广至3×3核。获得了3×3核内部最小计算单元的信息更新公式;基于信息更新公式,给出了3×3核的BP译码算法。仿真结果表明,对于3×3核极化码,BP译码算法相比于SC译码算法,在中低信噪比下性能要优于SC译码算法。在译码性能相当的条件下,BP译码算法有着更低的译码延时。

LDPC码的一种低复杂度BP译码算法

针对低密度奇偶校验(LDPC)码的BP译码算法在每一次迭代过程中,都要对全部比特和校验信息进行更新,存在计算量大、译码效率低的问题,提出了一种改进的BP译码算法.由于不同的比特节点和校验节点,其可靠程度不同,对BP译码的贡献也不同,为此给出了一种新的可靠性判断准则:采用每个比特的非法校验数和每次迭代过程中比特的伪后验概率的差来判断比特的可靠性,认为非法校验数小、伪后验概率差大的节点具有较高的可靠度.对可靠性较高的比特,下一次迭代过程中不参与更新,只更新那些有可能发生错误的比特.仿真结果表明,改进的BP译码算法在损失极少译码性能的情况下,大大地减少了迭代过程中的计算量,提高了译码效率.

LDPC码改进型LBP译码算法研究

针对LDPC(Low Density Parity Check)码分层(LBP:Layered Belief-Propagation)译码算法计算复杂度高、不易于硬件实现的问题,提出一种改进算法。该算法首先引入函数f(x)使LBP译码算法的计算复杂度大大降低;同时引入具体参数校正因子和偏移因子,提升译码性能。仿真结果表明,改进后的算法相比LBP算法在计算复杂度降低的同时,也提升了译码性能,从而达到了易于硬件实现的目的。

广义LDPC码的自适应全并行MAP-BP译码算法

提出了一种广义LDPC码的自适应全并行MAP-BP译码算法,算法中子码采用基于比特栅格的最大后验概率译码,本地码采用基于对数似然比的置信传播译码。算法引入自适应修正因子保证迭代过程中子码和本地码输出信息的匹配。仿真结果表明,与传统广义LDPC译码算法相比,MAP-BP算法可提高译码准确性并能加快译码收敛速度。

Beyond-BP译码算法综述:原理与应用

低密度奇偶校验码因其具有逼近香农限的优异性能,现已在多种标准和系统中得到广泛的应用。但为了使其能够满足不同应用场景下通信系统对纠错性能、计算复杂性、译码时延、硬件资源损耗以及功耗等方面的要求,需要对用于LDPC码译码的置信传播算法进行进一步的研究与改进。该文从译码算法的改进动机、方法论、计算复杂度以及性能表现等角度入手,对近些年出现的一些Beyond-BP译码算法进行了综述。并在最后对用于迭代接收系统的译码算法改进工作进行了讨论,为未来算法的改进工作提供一点思路。

基于可靠性更新的低复杂度BP译码算法

基于部分符号更新策略的BP(Belief Propagation)译码算法减少了LDPC(Low-Density Parity-Check)码的译码运算量,提高了译码效率。然而在其译码过程中,由于变量节点可靠性判决准确率不高,而且可靠性被误判的错误节点无法在后继的译码中得到修正,译码性能大大降低。该文提出一种改进的节点可靠性判决准则,提高迭代过程中对变量节点可靠性判断的准确率;同时,在每次迭代结束后,重新衡量所有变量节点的可靠性,以此来消除可靠性误判对译码性能的影响。仿真结果表明,改进的算法不仅使传统BP译码的复杂度降低,而且提高了BP算法的译码性能。

一种改进的LLR BP译码算法研究

运用LLR BP经典算法对低密度奇偶校验(LDPC)码译码时,由于译码时迭代次数过多和每次循环时校验节点的计算复杂度过高,导致译码复杂度非常高。提出了一种改进型LLR BP译码算法,采用泰勒级数将LLR BP算法中复杂度高的雅克比修正项进行分段线性近似。仿真表明:该算法在译码性能损失不大的情况下可大幅降低LDPC码的译码复杂度。

适用于BPSK系统的抗跳周LDPC译码算法

采用BPSK调制方式的系统发生跳周现象后,输入LDPC译码器的信息序列符号与原序列符号相反,导致译码器失效。提出了基于置信传播算法的抗跳周LDPC译码算法。该算法通过增加一次迭代译码的运算量,根据校验节点与变量节点之间传递的信息对初始似然比信息进行修正,可以消除跳周对译码器的影响。仿真结果表明在不发生跳周时,抗跳周LDPC译码算法与传统译码算法性能相同,即抗跳周LDPC译码算法对初始似然比信息的修正不会导致译码性能损失。在跳周发生时,传统译码算法失效。对校验节点奇数度的码字采用抗跳周译码算法可以完全克服跳周带来的影响,译码性能与无跳周发生时相同。

极化码BP译码算法中量化问题的研究

第五代移动通信(5G)面向高可靠和低时延的海量数据交互场景,如何实现其高效编译码方案是一个亟需解决的问题。现有编译码方案难以有效平衡译码过程中的计算复杂度和硬件实现难度,故无法应用于5G网络架构。针对该问题,提出了一种基于极化码的置信度传播(BP)译码量化方案。该方案结合最小和译码的近似算法和量化思想,显著降低了BP译码算法的计算复杂度和硬件实现难度。仿真成果表明,与最小和译码算法相比,量化后的BP译码算法极大地提高了译码性能。相比于BP译码算法,在几乎不降低译码性能的基础上,量化后的BP译码算法明显降低了计算复杂度,更便于硬件实现。

残差扰动网络辅助的BP译码算法

极化码的置信传播(Belief Propagation,BP)译码算法性能相比于其他极化码译码算法并不具有优势。为了改善这一现象,提出了一种基于残差网络和扰动译码算法相结合的BP译码算法。该算法通过在传统BP译码算法的基础上添加残差神经网络对接收信号进行处理,使其更大概率地落在可正确译码区域内,从而达到改善传统BP译码算法的译码性能的目的。仿真结果表明,在误比特率为10时,所提算法相比于传统的BP译码算法约有0.7 dB的性能增益,相比于BP-RNND(50)(BP-Residual Neural Network Decoder)译码算法约有0.6 dB的性能增益;同时,在低信噪比时所提算法的平均迭代次数相比于传统BP译码算法约有60%的降低。

一种利用ABP基于可信度迭代的RS码软译码算法

本文研究了自适应置信度传播和分阶统计译码的级联译码算法(ABP-OSD)。然后,我们把ABP-OSD算法和累积对数似然比(ALLR)算法进行结合,提出了一种RS码软译码算法ALLR-ABP-OSD。仿真结果表明,ALLR-ABP-OSD级联算法译码增益有所提高,在RS码译码性能和译码复杂度间取得了较好的折中。

改进型LLR BP译码算法研究

短低密度校验(LDPC)码的Tanner图中通常存在环路,变量节点之间的信息不再相互独立,导致LLR BP算法译码性能的下降。针对上述问题,提出一种改进型LLR BP译码算法,推导出有环时变量节点的真实信息,利用最小均方误差准则计算出有记忆的变量节点信息的权值,通过调整变量节点信息的迭代过程降低变量节点之间信息的相关性。仿真结果表明,改进型LLR BP算法具有比LLR BP算法、归一化BP算法及偏移量BP算法更好的LDPC译码性能。

短LDPC码和RS码基于BP算法的性能比较

LDPC码和RS码是目前2种较为常见的纠错编码,在深空通信方面有着广泛的应用。在相同码长和码率的情况下,对短LDPC码和RS码2种线性分组码在AWGN信道下进行了基于BP算法的性能比较。短LDPC码使用LLR-BP算法,RS码使用自适应置信度传播(ABP)算法。仿真结果表明,基于相同条件下,短LDPC码比较RS码表现出优越的译码性能。

LT码的一种BP／ML混合译码算法

针对LT码在短信息字长度时采用置信传播（BP）译码和最大似然（ML）译码存在大的性能差异问题，提出了一种BP／ML混合译码算法来实现Ⅱ码在二进制删除信道（BEC）中译码复杂度和性能的合理折中。此算法在BP译码失败时只需运用ML译码确定少数猜测比特就可实现成功译码。仿真结果显示，相比于BP译码，BP／ML混合译码的译码运行时间增加量少于50％，其仍远小于ML译码的译码运行时间。另一方面，BP／ML混合译码大大减少了译码失败概率，当译码开销大于10％时，BP／ML混合译码的性能接近于ML译码。

一种改进的Polar码的BP译码算法

为了减少置信度传播译码算法的计算复杂度,提出了一种改进的置信度传播译码算法.该算法在节点更新时,利用等误差的线性近似函数来代替算法中的双曲函数,相比于原始的置信度传播译码算法,改进的算法仅仅需要乘法和加法运算,因此大大降低了算法的计算复杂度,更易于硬件实现.仿真结果表明,在低信噪比时,改进的置信度传播译码算法的性能与原始BP译码算法的性能几乎相同,在高信噪比时,改进的置信度传播译码算法的性能比原始置信度传播译码算法的性能略差,在码长为256,误码率是10-6时,改进的置信度传播译码算法的误码率性能比原始的置信度传播译码算法退化了0.1dB.