Sequential message-passing decoding of LDPC codes by partitioning check nodes

In this paper, we analyze the sequential message- passing decoding algorithm of low-density parity-check (LDPC) codes by partitioning check nodes. This decoding algorithm shows better bit error rate (BER) performance than the conventional message-passing decoding algorithm, especially for the small number of iterations. Analytical results indicate that as the number of partitioned subsets of check nodes increases, the BER performance is improved. We also derive the recursive equations for mean values of messages at check and variable nodes by using density evolution with a Gaussian approximation. From these equations, the mean values are obtained at each iteration of the sequential decoding algorithm and the corresponding BER values are calculated. They show that the sequential decoding algorithm converges faster than the conventional one. Finally, the analytical results are confirmed by the simulation results.     

一种改进的无线光通信LDPC码译码算法

针对无线光通信中低密度奇偶校验码(LDPC)置信传播(BP)译码算法复杂度高及置信度振荡造成译码错误等缺点,基于对数BP算法提出了一种改进的译码算法。改进的译码算法在校验节点运算时,判断输入到校验节点消息的最小值与某个门限的大小,根据比较结果,分别用消息最小值或若干个最小值进行运算,在损失很少性能的情况下降低了运算复杂度;同时在比特节点采用振荡抵消处理运算,提高了算法的性能增益。最后在对数正态分布湍流信道模型下,分别对比特充分交织和交织深度为16的情况进行了仿真实验。仿真结果表明,改进的译码算法与BP算法相比,大幅度降低了计算复杂度,而且译码性能有一定的优势,收敛速度损失很少;而相对于最小和算法,改进的算法虽然译码复杂度有所增加,但误码率性能有明显的优势,并且收敛速度也优于最小和算法。因此,改进的译码算法是无线光通信中LDPC码译码算法复杂度和性能之间一个较好的折中处理方案。     

Efficient Difference-based Decoding Implementations of LDPC Codes

Efficient implementations of the sum-product algorithm (SPA) for decoding low-density parity-check (LDPC) codes using difference-based messages between bit nodes and check nodes are presented. As for the updates of check nodes, reduced- complexity derivatives are also put forward. As compared with the traditional Log-Likelihood-Ratio(LLR)-based decoding implementations, the proposed method has much lower complexity and latency, while it has no obvious loss of the error performance.     

改进的离散字母表迭代译码算法研究

为了优化LDPC迭代译码性能和降低算法复杂度,提出了一种改进的基于Gallager A算法的2b离散字母表迭代译码算法。在每一轮迭代中,Tanner图上的校验节点与变量节点之间所传递的消息有1b表示符号值,另1b反映码字结构特性,其中变量节点更新规则是通过查表法来实现的。在二元对称信道下针对列重为3的规则LDPC码做了仿真实验,仿真结果表明该算法性能明显优于原算法,并且具有较低的复杂度。     

基于串行消息传递机制的QC-LDPC码快速译码算法研究

针对准循环LDPC(QC-LDPC)码基于洪水消息传递机制译码算法的不足,该文提出了一种快速的分组串行译码算法。该算法通过将LDPC码的校验节点(或变量节点)按一定规则划分成若干个子集,在每一轮迭代过程中,依次对各个子集中的校验节点(或变量节点)并行地进行消息更新,提高了译码速度。同时根据分组规则,提出了一种有效的分组方法,并通过分析发现基于循环置换阵的准循环LDPC码非常适合采用这种分组译码算法进行译码。通过对不同消息传递机制下准循环LDPC码译码算法性能的仿真比较,验证了在复杂度不增加的情况下,该译码算法在继承了串行译码算法性能优异和迭代收敛快等优点的同时,极大地提高了准循环LDPC码的译码速度。分析表明,分组串行译码算法译码速度至少为串行译码算法的p倍(p为准循环LDPC码校验矩阵中循环置换阵的行数或列数)。     

基于SSCANL译码器的联合迭代检测译码算法

为了提升基于极化码的稀疏码多址接入（sparse code multiple access,SCMA）系统接收机性能,提出了基于简化软消除列表（simplify soft cancellation list,SSCANL）译码器的循环冗余校验（cyclic redundancy check,CRC）辅助联合迭代检测译码接收机方案。该方案中极化码译码器使用SSCANL译码算法,采用译码节点删除技术对软消除列表（soft cancellation list,SCANL）算法所需要的L次软消除译码（soft cancellation, SCAN）进行简化,通过近似删除冻结位节点,简化节点间软信息更新计算过程,从而降低译码算法的计算复杂度。仿真结果表明,SSCANL算法可获得与SCANL算法一致的性能,其计算复杂度与SCANL算法相比有所降低,码率越低,算法复杂度降低效果越好;且基于SSCANL译码器的CRC 辅助联合迭代检测译码接收机方案相较基于SCAN译码器的联合迭代检测译码（joint iterative detection and decoding based on SCAN decoder, JIDD-SCAN）方案、基于SCAN译码器的CRC辅助联合迭代检测译码（CRC aided joint iterative detection and decoding based on SCAN decoder,C-JIDD-SCAN）方案,在误码率为10^-4时,性能分别提升了约0.65 dB、0.59 dB。     

应用于无人机测控传输系统的多元LDPC码

针对无人机巡查区域地理环境复杂、信道特性多变、突发衰减严重的问题,设计了一种基于多元低密度奇偶校验( Q-LDPC)码的无人机测控传输系统。为减小置信传播( BP)类译码算法中振荡变量节点引入的错误传播,采用加权因子校正迭代前后的变量信息,从而减小短环对遥测、遥控等中短码字译码性能的影响,提高无人机测控传输系统可靠性。基于突发衰减信道建立系统仿真模型,仿真结果表明,所提方案通过将连续的突发比特错误转换为数量较小的符号错误,能够有效抵御快速衰落,降低误码率,为无人机对地观测提供安全保障。     

A novel decoding algorithm based on the hierarchical reliable strategy for SCG-LDPC codes in optical communications

An effective hierarchical reliable belief propagation （HRBP） decoding algorithm is proposed according to the struc- tural characteristics of systematically constructed Gallager low-density parity-check （SCG-LDPC） codes. The novel decoding algorithm combines the layered iteration with the reliability judgment, and can greatly reduce the number of the variable nodes involved in the subsequent iteration process and accelerate the convergence rate. The result of simulation for SCG-LDPC（3969,3720） code shows that the novel HRBP decoding algorithm can greatly reduce the computing amount at the condition of ensuring the performance compared with the traditional belief propagation （BP） algorithm. The bit error rate （BER） of the HRBP algorithm is considerable at the threshold value of 15, but in the sub- sequent iteration process, the number of the variable nodes for the HRBP algorithm can be reduced by about 70% at the high signal-to-noise ratio （SNR） compared with the BP algorithm. When the threshold value is further increased, the HRBP algorithm will gradually degenerate into the layered-BP algorithm, but at the BER of 10-7 and the maximal iteration number of 30, the net coding gain （NCG） of the HRBP algorithm is 0.2 dB more than that of the BP algo- rithm, and the average iteration times can be reduced by about 40% at the high SNR. Therefore, the novel HRBP de- coding algorithm is more suitable for optical communication systems.     

光传输系统中一种新颖的SCG-LDPC码译码算法分析

依据SCG-LDPC码的结构特点提出了一种高效的分层可靠置信传播(HRBP)译码算法,该算法结合分层迭代与可靠度判决测量有效降低后续迭代过程中的变量节点数,同时加快了收敛速度。针对适用于光传输系统的SCG-LDPC(3 969,3 720)码进行仿真,仿真结果表明HRBP算法与传统的BP算法相比,在保证性能的同时大大降低了运算量,在阈值为15时,HRBP译码算法误码率性能与BP译码算法相当,但是后续迭代的变量节点数在高信噪比下相比BP译码算法减少约69%,当阈值进一步增大时,HRBP算法将逐步退化为分层置信传播(Layered-BP)译码算法。     

基于分布式奇偶校验码的低复杂度极化码SCLF译码算法

针对极化码串行抵消列表比特翻转(Successive Cancellation List Bit-Flip, SCLF)译码算法复杂度较高的问题,提出一种基于分布式奇偶校验码的低复杂度极化码SCLF译码(SCLF Decoding Algorithm for Low-Complexity Polar Codes Based on Distributed Parity Check Codes, DPC-SCLF)算法。与仅采用循环冗余校验(Cyclic Redundancy Check, CRC)码校验的SCLF译码算法不同,该算法首先利用极化信道偏序关系构造关键集,然后采用分布式奇偶校验(Parity Check, PC)码与CRC码结合的方式对错误比特进行检验、识别和翻转,提高了翻转精度,减少了重译码次数。此外,在译码时利用路径剪枝操作,提高了正确路径的竞争力,改善了误码性能,且利用提前终止译码进程操作,减少了译码比特数。仿真结果表明,与D-Post-SCLF译码算法和RCS-SCLF译码算法相比,所提出算法具有更低的译码复杂度且在中高信噪比下具有更好的误码性能。     

LDPC Decoding by Failed Check Nodes for Serial Concatenated Code

The use of serial concatenated codes is an effective technique for alleviating the error floor phenomenon of low‐density parity‐check (LDPC) codes. An enhanced sum–product algorithm (SPA) for LDPC codes, which is suitable for serial concatenated codes, is proposed in this paper. The proposed algorithm minimizes the number of errors by using the failed check nodes (FCNs) in LDPC decoding. Hence, the error‐correcting capability of the serial concatenated code can be improved. The number of FCNs is simply obtained by the syndrome test, which is performed during the SPA. Hence, the decoding procedure of the proposed algorithm is similar to that of the conventional algorithm. The error performance of the proposed algorithm is analyzed and compared with that of the conventional algorithm. As a result, a gain of 1.4 dB can be obtained by the proposed algorithm at a bit error rate of 10^?8. In addition, the error performance of the proposed algorithm with just 30 iterations is shown to be superior to that of the conventional algorithm with 100 iterations.     

对LDPC码的LLRBP算法研究

在LDPC译码时,使用IJLRBP算法其校验节点的计算复杂度十分高,而且当LDPC码中有许多的短环时,译码性能也会降低。基于以上的这些问题提出了一个新的混合校验变量过程,通过调整校验节点的处理振幅和变量节点的信息相关性来降低计算复杂度,其仿真过程表明在译码性能和运算复杂度上与LLRBP算法都有较大的提高。     

基于振荡迭代的修正BP译码算法

针对中高信噪比(SNR)下低密度奇偶校验(LDPC)译码错误振荡迭代不收敛,提出了基于置信传播(BP)算法的修正LDPC译码算法,即软值归零BP算法。该算法通过将振荡迭代的变量节点传递的外信息置零,减少错误信道消息对迭代译码的影响,较大地改善了译码性能。而且,还给出了振荡迭代节点的判定准则,提高了振荡迭代节点判定的准确性。仿真结果表明,在中高信噪比区且译码迭代次数相同的情况下,该算法能比BP算法获得更好的译码性能。     

一种联合星座和伴随式信息的迭代译码算法

针对构造性的大数逻辑可译低密度奇偶校验(LDPC)码,联合信号星座和伴随式信息,提出一种基于可靠度的迭代大数逻辑译码算法。在校验节点,直接使用伴随式信息进行传递和处理;在变量节点,结合信源端的星座映射和伴随式进行译码信息收集和处理。理论分析和仿真实验结果表明,所提出的算法在保持优良译码性能的同时,具有更低的译码复杂度。     

一种动态加权的LDPC译码方法

为了加快低密度奇偶校验（LDPC）码的译码速度,有效改善LDPC码的译码性能,针对校验节点更新过程中的对数似然比（LLR）值的大小,设计了一种LDPC码的动态加权译码方法。以IEEE 802.16e标准的奇偶校验矩阵为例,根据LLR值的变化规律,利用增长因子和抑制因子对和积译码算法和最小和译码算法进行动态加权。仿真结果显示,基于动态加权的译码方法相对于传统译码方法误码率都有明显改进,译码复杂度也有所降低。     

低复杂度的TBCC自适应循环VA译码算法

咬尾是一种将卷积码转换为块码的技术,它消除了归零状态所造成的码率损失,同时避免了截尾带来的性能降低,在短块编码中具有明显优势.针对咬尾卷积码(TBCC)现有译码算法复杂度过大和收敛性问题,提出一种低复杂度的TBCC自适应循环维特比(VA)译码算法.该算法根据信道变化自适应调整译码迭代次数,使咬尾路径收敛到最佳.通过仿真...     

系统RA码的基于WBF策略的改进BP译码算法

 针对重复累积(RA)码译码算法(BP算法和最小和算法)复杂度高或纠错性能下降的问题,将加权位翻转WBF的思想用于改进BP算法,提出了基于WBF策略的改进BP译码算法. 在每次迭代译码中若未能译出合法码字,则按一定规则进行位翻转操作,以期获得合法码字. 仿真结果表明,本算法能有效降低系统RA码的运算复杂度,且能保持优异的译码性能.     

LDPC短码的编译码研究

这里研究了原模图LDPC码和BP译码算法,首先提出了一种基于PEG算法构造原模图LDPC码的算法,该码字在码率为1/2,码长256比特的情况下,译码性能超过了PEG算法,然后针对LDPC短码不可避免存在四环的特殊性,提出了一种修正四环中变量节点迭代信息的BP译码改进算法,使得具有四环的LDPC短码的译码性能得到较大提升。     

Turbo decoding of product codes using adaptive belief propagation

The adaptive belief propagation (ABP) algorithm was recently proposed by Jiang and Narayanan for the soft decoding of Reed-Solomon (RS) codes. In this paper, simplified versions of this algorithm are investigated for the turbo decoding of product codes. The complexity of the turbo-oriented adaptive belief propagation (TAB) algorithm is significantly reduced by moving the matrix adaptation step outside of the belief propagation iteration loop. A reduced-complexity version of the TAB algorithm that offers a trade-off between performance and complexity is also proposed. Simulation results for the turbo decoding of product codes show that belief propagation based on adaptive parity check matrices is a practical alternative to the currently very popular Chase-Pyndiah algorithm.     

Generalized Low-Density Parity-Check Codes Based on Hadamard Constraints

In this paper, we consider the design and analysis of generalized low-density parity-check (GLDPC) codes in AWGN channels. The GLDPC codes are specified by a bipartite Tanner graph, as with standard LDPC codes, but with the single parity-check constraints replaced by general coding constraints. In particular, we consider imposing Hadamard code constraints at the check nodes for a low-rate approach, termed LDPC-Hadamard codes. We introduce a low-complexity message-passing based iterative soft-input soft-output (SISO) decoding algorithm, which employs the a posteriori probability (APP) fast Hadamard transform (FHT) for decoding the Hadamard check codes at each decoding iteration. The achievable capacity with the GLDPC codes is then discussed. A modified LDPC-Hadamard code graph is also proposed. We then optimize the LDPC-Hadamard code ensemble using a low-complexity optimization method based on approximating the density evolution by a one-dimensional dynamic system represented by an extrinsic mutual information transfer (EXIT) chart. Simulation results show that the optimized LDPC-Hadamard codes offer better performance in the low-rate region than low-rate turbo-Hadamard codes, but also enjoy a fast convergence rate. A rate-0.003 LDPC-Hadamard code with large block length can achieve a bit-error-rate (BER) performance of 10^-5 at -1.44 dB, which is only 0.15 dB away from the ultimate Shannon limit (-1.592 dB) and 0.24 dB better than the best performing low-rate turbo-Hadamard codes