RS码与LDPC码的联合迭代译码

针对RS码与LDPC码的串行级联结构,提出了一种基于自适应置信传播(ABP)的联合迭代译码方法.译码时,LDPC码置信传播译码器输出的软信息作为RS码ABP译码器的输入;经过一定迭代译码后,RS码译码器输出的软信息又作为LDPC译码器的输入.软输入软输出的RS译码器与LDPC译码器之间经过多次信息传递,译码性能有很大提高.码长中等的LDPC码采用这种级联方案,可以有效克服短环的影响,消除错误平层.仿真结果显示:AWGN信道下这种基于ABP的RS码与LDPC码的联合迭代译码方案可以获得约0.8 dB的增益.     

Reduced-Complexity Decoding of LDPC Codes

Reduced-Complexity Decoding of LDPC Codes Various log-likelihood-ratio-based belief-propagation (LLR- BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representation of the decoding computations are shown to achieve a reduction in complexity, by simplifying the check-node update or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from a performance, latency, computational complexity, and memory-requirement perspective.     

低密度校验码量化译码研究

介绍了基于置信传播算法的LDPC码和积译码算法，分析其密度进行化特性，对不同消息空间中的量化译码问题进行研究，对采用不同量化方案时LDPC码在AWGN信道下的译码性能进行了仿真。仿真结果表明相对连续译码，中间变量6bit均匀量化会带来约0．4dB左右的损失，而10bit非均匀量化性能明显得到改善。合适的高阶量化译码可以获得接近连续译码的性能。     

基于大数逻辑可译LDPC码的译码算法研究

本文提出两种基于可靠度的迭代大数逻辑译码算法,从以下两个方面降低译码复杂度:(1)校验节点使用伴随式信息处理,可节省外信息的计算操作;(2)变量节点使用伴随信息进行总信息的投票计数过程.结合非均匀量化技术,接收信号在判决门限附近获得更加精细的处理.此外,本文利用量化参数和列重比例信息对可靠度偏移方向和幅度进行了设计.仿真实验表明,本文提出的算法能够在很低的量化比特(3~4 bits)下有效工作,具有优良的译码性能和快速的收敛速度.     

Enhanced Verification-Based Decoding for Packet-Based LDPC Codes

In this letter, an enhanced verification-based decoding algorithm (EVA) for packet level low-density parity-check (LDPC) codes is proposed. Compared with the verification algorithm (VA) in the literature, the proposed algorithm reduces the likelihood of false verification by enhancing the verification condition to achieve a better decoding performance. For example, simulation results in this letter show that EVA reduces frame error rate (FER) by two orders when comparing the VA over binary symmetric channel (BSC), while the increase of the computational load is less than 90%.     

LDPC卷积码的快速收敛译码

采用串行消息传递策略,文中提出了LDPC卷积码的一种改进的流水线式译码器.分析和仿真结果均表明改进的译码器在不增加单个处理器计算复杂度的前提下,仅通过改变消息传递方式就能够大大加速译码收敛速率,与原译码器相比大约可以节省一半的处理器.     

Gradient Projection Decoding of LDPC Codes

A new practical method for decoding low-density parity check (LDPC) codes is presented. The followed approach involves reformulating the parity check equations using nonlinear functions of a specific form, defined over R^rho, where rho denotes the check node degree. By constraining the inputs to these functions in the closed convex subset [0,1]^rho ("box" set) of R^rho, and also by exploiting their form, a multimodal objective function that entails the code constraints is formulated. The gradient projection algorithm is then used for searching for a valid codeword that lies in the vicinity of the channel observation. The computational complexity of the new decoding technique is practically sub-linearly dependent on the code's length, while processing on each variable node can be performed in parallel allowing very low decoding latencies. Simulation results show that convergence is achieved within 10 iterations, although some performance degradations relative to the belief propagation (BP) algorithm are observed     

LDPC码的级联译码算法的改进与实现

针对中短码长中LDPC码的OSD串行级联译码算法,给出了一种FPGA实现方案。该方案基于FPGA芯片中的块RAM资源,实现了OSD译码中GF(2)上的高斯消元算法,避免了其对逻辑资源的大量消耗。结果表明,该实现方案可在中低端FPGA上实现500 kbit·s^-1吞吐量的LDPC码OSD串行级联译码器。     

一种低复杂度的LDPC码迭代译码算法

在LDPC码的译码算法中，和积算法性能最优但复杂性较高，最小和算法实现简单但性能与和积算法相差较多。针对这一性能与复杂度的矛盾，带有修正项的最小和算法成为研究的热点问题。文中基于一种性能与和积算法接近的修正最小和算法进行研究，对修正项的修正方式进行了简化，简化后的算法在性能上与和积算法仍非常接近，实现复杂度却比原修正最小和算法有明显的降低。     

多进制LDPC译码算法的研究

多进制LDPC码是将二进制LDPC码推广到有限域GF（q）,其校验矩阵的元素不再是（0,1）,而是集合（0,1,…,q-1）,译码仍然采用高效的基于置信度传播的迭代译码算法。这里主要推导了多进制译码算法的迭代公式,分析证明了基于快速傅里叶变换（FFT）理论的改进算法,最后通过仿真手段验证和分析了基于FFT的多进制译码算法的优越性能。     

空间耦合LDPC码的分层译码算法

针对长码长空间耦合低密度奇偶校验(SC-LDPC)码译码时延较长的问题,该文提出了分层滑动窗译码(LSWD)算法。该算法利用SC-LDPC子码码块的准循环特性和滑动窗内校验矩阵的层次结构,通过在滑动窗内对校验矩阵进行分层处理,优化层与层之间消息传递,从而加快窗内译码的收敛速度,减少了译码迭代次数。仿真和分析结果表明：在相同的信噪比(SNR)条件和相同的误码性能要求下,LSWD算法所需的迭代次数少于滑动窗译码(SWD)算法,特别在高信噪比下,LSWD算法的迭代次数约为SWD算法的一半,从而有效缩短全局译码时延;在相同译码迭代次数下,LSWD算法的译码性能优于SWD算法,而其计算复杂度增加不大。

     

一种多进制LDPC码加权符号翻转译码算法

提出了一种低复杂度基于翻转规则的多进制低密度奇偶校验(Low-Density Parity-Check ,LDPC)码符号翻转译码算法。为寻求有效码字,该算法在符号向量空间迭代地更新硬判决的接收符号向量。每一次迭代只改变一个符号,其符号翻转函数综合考虑了不满足校验式的个数和接收比特和计算出符号的可靠性度量。在高阶伽罗华域中采用一种无限环路规避和翻转符号选取方法,同时提出了翻转规则设计方法,该设计决定了计算复杂度和差错性能。仿真结果表明,该符号翻转算法在帧长为150符号的16进制LDPC码中取得了纠错性能和计算复杂度的有效权衡。     

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.     

适于分层译码算法的LDPC码构造方法

The layered decoding algorithm has been widely used in the implementation of Low Density Parity Check (LDPC) decoders, due to its high convergence speed. However, the pipeline operation of the layered decoder may introduce memory access conflicts, which heavily deteriorates the decoder throughput. To essentially deal with the issue of memory access conflicts, we propose a construction algorithm of LDPC codes, to which a constraint condition is added in the Progressive Edge-Growth (PEG) algorithm. The constraint condition can guarantee that for our constructed LDPC codes, the sets of all the variable nodes connected to the consecutive layers do not share any common variable node, which can avoid the memory access conflicts. Simulation results show that the performance of our constructed LDPC codes is close to the several other LDPC codes adopted in wireless standards. Moreover, compared with the decoder for IEEE 802. 16e LDPC codes, the throughput of our LDPC decoder has large improvement, while the chip resource consumption is unchanged. Thus, our constructed LD-PC codes can be adopted in the high-speed transmission.     

Memory-Efficient and High-Throughput Decoding of Quasi-Cyclic LDPC Codes

We propose turbo-sum-product (TSP) and shuffled-sum-product (SSP) decoding algorithms for quasi-cyclic low-density parity-check codes, which not only achieve faster convergence and better error performance than the sum-product algorithm, but also require less memory in partly parallel decoder architectures. Compared with the turbo decoding algorithm, our TSP algorithm saves the same amount of memory and may achieve a higher decoding throughput. The convergence behaviors of our TSP and SSP algorithms are also compared with those of the SP, turbo, and shuffled algorithms by their extrinsic information transfer (EXIT) charts.     

LDPC编译码技术研究

LDPC码,即低密度奇偶校验码,本质上是一种线性分组码,其译码性能比Turbo码更接近香农限。文中首先介绍了LDPC码的定义及描述;其次对LDPC码快速编码方法进行分析,对可线性编码的LDPC码构造进行探讨;然后对LDPC的译码技术进行研究;最后对LDPC码的应用前景进行讨论。     

一种LDPC编码高阶调制系统的联合解调解码方法

该文用一种级联码模型描述了LDPC编码高阶调制系统。该级联码模型以LDPC码为外码,二-十进制转换码为内码,再加一个删余模块构成。基于这种级联码模型,该文给出了其联合校验方程和二分图,并提出了级联码置信度传播算法,实现了LDPC编码高阶调制系统的联合解调解码。仿真表明,该文提出的联合解调解码算法有效地改进了LDPC编码高阶调制系统的性能。     

一种基于分层译码和Min-max的多进制LDPC码译码算法

该文在现有译码算法的基础上提出一种高效的非二进制低密度奇偶校验码(NB-LDPC)译码方法,充分利用了分层译码算法与Min-max算法的优点,不但译码复杂度低、需要的存储空间小,而且可将译码速度提高一倍。应用该算法,对一种定义在GF(25)上的(620,509)码进行了仿真。该码的仿真结果表明：在相同误码率下,该文译码算法所需最大迭代次数仅为Zhang的算法(2011)的45%。     

一种应用于不可分层LDPC码的并行分层译码算法

该文针对不可分层LDPC码无法利用分层算法进行译码的问题,提出了一种并行分层置信度传播(Parallel-Layered Belief-Propagation,PLBP)译码算法。与传统分层算法不同,该算法在译码时并行进行各层更新,串行进行层内各行更新。这种译码机制使得同一变量节点在各层内不同时进行更新,从而实现各变量节点在一次迭代中分层递进更新的算法目标。仿真表明,在不增加译码复杂度的情况下,该文提出的PLBP算法与传统的洪水算法相比,误码性能更优,而且所需要的平均迭代次数降低了约50%。此外,PLBP算法采用了合并的节点更新运算,最终使该算法达到的译码速度约为洪水算法的4倍。     

LDPC码加权比特翻转译码算法研究

近年来,基于置信传播(BP),最小和(MS)和归一化最小和(NMS)算法,已经提出3种相对应的LDPC码加权比特翻转(WBF)译码算法。但这3种WBF算法所代表的物理意义和内在的紧密联系问题目前仍未有所研究。该文依据一种全新的理解方式,对3种WBF算法进行理论推导,并阐述3种算法内在的紧密联系,最后通过仿真验证所得结论的合理性和正确性。这对于设计新的改进型WBF算法具有一定的指导意义。