RS码的编译码程序实现

RS码是一种对随机和突发差错具有良好纠错能力的多进制信道编码。文中介绍了RS码编码和BM迭代译码的原理,推导了在程序实现时关键步骤的迭代表达式,并采用C语言实现了构造伽罗华域、RS码生成多项式、RS码编码和BM迭代译码算法。程序可通过配置RS码码长、信息位长等参数完成对多种RS码的编译码,适用于包含多种RS系统码及截短码通信系统的编译码,具有工程应用价值。     

基于GPU的RS码并行译码算法研究

针对RS码硬件译码器中常用的BMA译码算法并行性较差,导致译码延迟较大和译码速率较低的问题,研究了RS码的高速并行译码算法及其软件实现方式,设计和实现了一种基于GPU的RS码并行译码算法cu PGZ。实验结果表明,对CCSDS建议的RS(255,223)码,在128 bits错误的情况下,cu PGZ可以达到590 Mbps的最大译码速率以及0.5 ms的最小译码延迟,与BMA算法的GPU实现相比,译码速率提高1倍,译码延迟降低为1/60。实际工程应用表明,cu PGZ能够满足实际测控数传的信道译码要求。     

广义RS码的子域子码的超距离译码

Delsarte在文献[1]中建立了广义RS码的子域子码,它既包括了BCH码,广义BCH码,也包括了Goppa码,并得出最小距离下限扩张的一般定理。为了充分利用广义RS码的子域子码的纠错能力,设计广义RS码的子域子码的超设计距离译码器是十分有意义的。本文指出,用解线性方程组的方法可实现对广义RS码的子域子码的超距离译码。从而,BCH码、GBCH码、Goppa码的超距离译码问题一起被解决了。     

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.     

一种新的缩短RS码迭代译码方案

为了在EPON中应用GF(256)标准RS码对信息帧长大于255位的信息流进行编码,并提高RS码的编码增益,提出了一种新的缩短RS码的编译码方案。该方案通过两个缩短RS码的交叠编码和互相迭代译码,可以提高编译码增益。RS码BM硬判决译码和chase软判决译码的计算机仿真表明,该方案对缩短RS码的软硬判决译码性能都有明显提高。     

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泽码的级联译码算法(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.     

实现Reed-Solomon码译码的新电路--在普通基上用"比特串行乘法电路"实现RS码译码

本文推出了在域GF(2m)上用于RS码译码的两种新电路:普通基"比特串行序列乘法电路"和"比特串行乘法累加电路",基本上以m个与门代替了两个任意元素相乘的复杂乘法器,使译码电路大大简化.作为一个应用实例,详细阐明了用它们构造的RS码纠删/纠错译码各步电路.这两种新电路对性能优良的RS码的使用和推广具有实用价值.     

RS/LT级联编码在DVB广播中的应用

提出了一种改进的RS/LT级联编码构造方法,并分析了其在基于DVB广播中的应用.分析了RS-LT级联编码相对传统LT码在提高可译码概率方面的优点.仿真结果表明,该方法提高了LT码在相同编码冗余度下的可译码概率,降低了LT码在一定可译码概率下的编码冗余度要求.应用RS/LT级联码方法,可以减小DVB广播中因为媒体流失同步而导致的画面阻塞,具有很好的应用前景.     

Reed-Solomon码性能增强译码算法

Reed-Solomon (RS)码具有优良的纠随机错误和突发错误的能力,被广泛应用于通信系统中。依据RS码定义的计算映射与按BCH子码编码2种不同的编码方式,对RS码性能增强算法进行了分类总结,并对比了这2类性能增强算法的异同。仿真结果表明,相对于传统的BMA译码算法,在误帧率为10-3时,KV算法可以提升RS码0.35 d B的性能增益,Chase译码算法有大约0.65 d B的增益,指出了RS码性能增强算法中Chase列表译码算法的后续研究方向。     

一种应用于DMB-T的基于RS码软判决译码的级联码方案

结合DMB—T系统的信道编码方案以及编码领域的最新进展,即RS码软判决译码算法的发展,提出了一种应用于DMB-T系统基于和积算法(SPA)的RS码软判决译码的级联码方案。该方案仅需在现有方案的基础上作少量调整即可获得可观的编码增益。和其它流行的软判决译码算法的比较表明,此方案提出的RS码软判决译码算法在DMB-T系统的应用中具有一定的优势。     

Soft decision decoding of Reed-Solomon codes

This paper presents a maximum-likelihood decoding (MLD) and a suboptimum decoding algorithm for Reed-Solomon (RS) codes. The proposed algorithms are based on the algebraic structure of the binary images of RS codes. Theoretical bounds on the performance are derived and shown to be consistent with simulation results. The proposed suboptimum algorithm achieves near-MLD performance with significantly lower decoding complexity. It is also shown that the proposed suboptimum, algorithm has better performance compared with generalized minimum distance decoding, while the proposed MLD algorithm has significantly lower decoding complexity than the well-known Vardy-Be'ery (1991) MLD algorithm.     

On the performance and complexity of A generalized minimum distance reed–solomon decoding algorithm

The article reports on the characteristics of an algorithm that implements generalized minimum distance (GMD) decoding of Reed-Solomon codes. The algorithm uses the novel Welch-Berlekamp (WB) algorithm, as modified by Tze-Hua, in order to minimize the complexity of the decoder. Both the WB algorithm and the GMD extension of the WB algorithm are described in outline. The performance of the GMD algorithm was simulated on AWGN channels and fading channels. Results are presented both for RS and concatenated RS codes. The gains over conventional decoding are larger for fading channels than for AWGN conditions but seem useful in all cases. The complexities of the GMD algorithm and the WB algorithm are analysed and compared to that of conventional RS decoding algorithms.     

光存储RS译码器设计与译码速度分析

比较了reed-solomon（RS）译码的Berlekamp-Massey（BM）算法和Euclidean算法的运行速度,并选择BM算法设计了满足36Mbps数据传输率（D豫）的RS译码器。针对现有几种光盘的DTR,进一步分析了光存储中RS译码速度的要求,并对译码中的有限域乘法器做了仿真。该乘法器在工作频率为50MHz的FPGA芯片中工作正常,可以满足光盘的DTR要求。     

Erased-Chase decoding for RS-coded MPSK signaling over a Rayleigh fading channel

In this paper, a novel dual-metric, the maximum and minimum Squared Euclidean Distance Increment （SEDI） Brought by changing the hard decision symbol, is introduced to measure the reliability of the received M-ary Phase Shift Keying （MPSK） symbols over a Rayleigh fading channel. Based on the dual-metric, a Chase-type soft decoding algorithm, which is called erased-Chase algorithm, is developed for Reed-Solomon （RS） coded MPSK schemes. The proposed algorithm treats the unreliable symbols with small maximum SEDI as erasures, and tests the non-erased unreliable symbols with small minimum SEDI as the Chase-2 algorithm does. By introducing optimality test into the decoding procedure, much more reduction in the decoding complexity can be achieved. Simulation results of the RS（63, 42, 22）-coded 8-PSK scheme over a Rayleigh fading channel show that the proposed algorithm provides a very efficient tradeoff between the decoding complexity and the error performance. Finally, an adaptive scheme for the number of erasures is introduced into the decoding algorithm.     

On acceptance criterion for efficient successiveerrors-and-erasures decoding of Reed-Solomon and BCH codes

We describe an efficient algorithm for successive errors-and-erasures decoding of BCH codes. The decoding algorithm consists of finding all necessary error locator polynomials and errata evaluator polynomials, choosing the most appropriate error locator polynomial and errata evaluator polynomial, using these two polynomials to compute a candidate codeword for the decoder output, and testing the candidate for optimality via an originally developed acceptance criterion. Even in the most stringent case possible, the acceptance criterion is only a little more stringent than Forney's (1966) criterion for generalised minimum distance (GMD) decoding. We present simulation results on the error performance of our decoding algorithm for binary antipodal signals over an AWGN channel and a Rayleigh fading channel. The number of calculations of elements in a finite field that are required by our algorithm is only slightly greater than that required by hard-decision decoding, while the error performance is almost as good as that achieved with GMD decoding. The presented algorithm is also applicable to efficient decoding of product RS codes     

DVB-S中RS译码的快速算法

本文介绍了DVB-S中RS码的编码及常用的译码算法,然后又介绍了几种有限域中快速傅里叶变换(FFT)算法。提出了一种快速频域译码算法,该算法用速度较快的Good-ThomasFFT和素数域中的半快速算法来优化频域译码算法,使DVB-S中(204,188)RS码的译码速度提高了近10倍。     

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。     

非系统RS(31,19)编译码算法研究与FPGA实现

针对战术数据链系统低时延数据传输需求,提出一种适用于数据链系统的信道编码方案—非系统缩短码RS(31,19)。本文从MS多项式的观点讨论了非系统RS码的编码和译码算法,并对缩短RS码的编译码算法进行了研究。最后在FPGAEP3SE110上采用了一种改进的BM算法,成功实现RS(31,19)编译码复杂算法,有效提高了译码速度,简化了数据链系统硬件设计。     

Hard- and soft-decision decoding beyond the half minimum distance---An algorithm for linear codes (Corresp.)

A decoding algorithm for linear codes that uses the minimum weight words of the dual code as parity checks is defined. This algorithm is able to correct beyond the half minimum distance and has the capability of including soft-decision decoding. Results on applying this algorithm to quadratic residue (QR) codes, BCH codes, and the Golay codes (with and without soft-decision decoding) are presented.     

RS码译码算法对比研究

RS码所具有的高效译码性能使其被广泛应用于数据通信和存储系统的差错控制中。本文主要对目前常用的RS码的硬判决译码算法和K—V代数软判决译码算法进行对比研究。通过对两种算法原理的理论分析,给出了RS码在硬判决与软判决的算法下的计算机仿真。结果表明两种算法均能得到良好的译码效果,而软判决译码算法较硬判决方式能更有效地带来系统增益。而软判决译码算法可以通过适当提高复杂度来改善系统的性能。