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。     

时域Reed—Solomon译码器及其在FPGA上的实现

基于Blahut提出的RS（Reed-dSolomon）码时域译码算法,提出了一种时域RS译码器,详细讨论了FPGA（现场可编程门阵列）实现该译码器的过程,并以六进制RS(63,47）码为例对用FPGA实现的RS译码器性能进行了分析,该译码器输入码流速率可达6Mbit/s,占用的FPGA（Spartan Ⅱ系列）的资料不到相应频译译码器的一半。     

RS译码的BM迭代算法及其FPGA实现

介绍了运用于RS译码中的BM迭带算法及利用BM迭带进行RS译码的基本原理,同时给出了该算法的FPGA实现,并通过在高清晰度数字电视接收机中验证了设计的可行性与可靠性。     

DVB标准RS码译码的新技术

根据RS译码算法原理[1] ,结合DVB(数字视频广播 )系统中译码的具体指标要求以及芯片模块化的思想 ,通过对BM算法实现的优化和改进 ,采用FPGA技术实现了RS译码电路 ,通过了QUAR TUSII仿真测试以及试验板调试。由于采用了流水线技术、新的无求逆的BM算法以及关键环节的优化设计 ,使得该译码器速度快 ,占用资源少 ,译码速率可达 2 0Msps。     

DVB标准RS码译码的新技术

根据RS译码算法原理[1],结合DVB(数字视频广播)系统中译码的具体指标要求以及芯片模块化的思想,通过对BM算法实现的优化和改进,采用FPGA技术实现了RS译码电路,通过了QUARTUSII仿真测试以及试验板调试.由于采用了流水线技术、新的无求逆的BM算法以及关键环节的优化设计,使得该译码器速度快,占用资源少,译码速率可达20 Msps.     

基于FPGA的RS译码器的设计与实现

针对Reed-Solomon（RS）码译码过程复杂、译码速度慢和专用译码器价格高等问题,以联合信息分发系统终端J系列报文信息位采用的RS（31,15）码为例,介绍了基于改进的无求逆运算的Berlekamp-Massey（BM）迭代算法的RS译码原理,采用Verilog硬件描述语言对译码器中各个子模块进行了设计,并基于现场可编程门阵列平台,在QuartusII6.0环境下进行了仿真,验证了RS译码器的纠错能力,实现了参数化与模块化的RS译码器设计。     

DVB标准RS码译码的新技术

根据RS译码算法原理[1],结合DVB(数字视频广播)系统中译码的具体指标要求以及芯片模块化的思想,通过对BM算法实现的优化和改进,采用FPGA技术实现了RS译码电路,通过了QUARTUSII仿真测试以及试验板调试.由于采用了流水线技术、新的无求逆的BM算法以及关键环节的优化设计,使得该译码器速度快,占用资源少,译码速率可达20 Msps.     

RS译码的Euclid算法及其FPGA实现

介绍运用于RS译码中的Euclid算法及利用Euclid算法进行RS译码的基本原理，同时给出该算法的FPGA实现，并在高清晰度数字电视接收机中验证了设计的可行性与可靠性。     

JTIDS中的RS（31，15）编译码器设计及性能分析

为提高抗干扰能力,JTIDS在数据部分采用了RS（31,15）编译码。在分析了RS码本原多项式及生成多项式的基础上,构建了RS（31,15）的伽罗华域,给出RS（31,15）的编／译码的具体算法。在Simulink仿真平台上对RS（31,15）的编／译码过程实现了仿真。通过仿真结果,具体分析了RS（31,15）的抗干扰性能。     

RS码的译码算法及软件实现

针对RS码译码比较复杂的特点，详细介绍了RS码译码的过程和算法，并通过实例说明其软件实现方法。     

一种高效RS编解码器的FPGA实现

提出了一种实现复杂度低、高效率的RS(204,188)编解码器的FPGA实现电路.整个FPGA设计分为RS编码器、Homer准则的伴随式计算、改进的BM算法、Chien搜索求根和Forney算法求差错幅值等5个模块,同时,总体电路采用了pipeline结构,有效提高了译码速率.选用Xilinx公司的Spartan3E系列XC3S500E芯片,译码时延242个时钟周期,使用FPGA资源186000门,译码性能与理论值一致,已用于特定无线图像传输系统.     

一种基于FPGA的RS编译码器设计与实现

RS码是线性分组码中具有很强纠错能力的多进制BCH码,其在纠正随机错误和突发错误方面非常有效,因此被广泛应用于通信和数据存储系统。本文提出了一种实现复杂度低、高效率的RS编译码器实现电路,包含RS编码器、Horner准则的伴随式计算、BM算法、Chien搜索等模块,以RS(15,9)为例运用VHDL在ISE14.6软件环境下进行了功能仿真,结果与Matlab得到的理论结果一致。该方法适用于任意长度的RS编码,有着重要的应用价值。     

The fast decoding of Reed-Solomon codes using Fermat theoretic transforms and continued fractions

It is shown that Reed-Solomon (RS) codes can be decoded by using a fast Fourier transform (FFT) algorithm over finite fieldsGF(F_{n}), whereF_{n}is a Fermat prime, and continued fractions. This new transform decoding method is simpler than the standard method for RS codes. The computing time of this new decoding algorithm in software can be faster than the standard decoding method for RS codes.     

Pattern-Flipping Chase-Type Decoders with Error Pattern Extracting Viterbi Algorithm over Partial Response Channels

Towards the goal of achieving better error correction performance in data storage systems, iterative soft decoding of low density parity check (LDPC) codes and soft-decision decoding of Reed-Solomon (RS) codes have started receiving increasing research attention. However, even with increased computing power, complexities of soft-decision decoding algorithms are still too high for real products which require high throughput and small hardware area. Another problem is that the performance gains of those approaches are smaller for magnetic recording channels than they are for memoryless additive white Gaussian noise (AWGN) channels. We propose a new soft-decision decoding algorithm (based on the Chase algorithm), which takes advantage of pattern reliability instead of symbol reliability or bit reliability. We also present a modified Viterbi algorithm that provides probable error patterns with corresponding reliabilities. Simulation results of the proposed algorithms over the partial response (PR) channel show attractive performance gains. The proposed algorithm dramatically reduces the number of iterations compared to the conventional Chase2 algorithm over the PR channel.     

光存储中RS纠错码两种实现算法的研究

以光存储应用为背景,针对盘片记录信息固有的高原生误码率问题,从目前CD,DVD的纠错编码方案出发,设计并实现一种合适的差错控制方法来保证数据读写的正确性。分析了实现Reed Solomon(RS)纠错编码的Berlekamp Massey(BM)算法和Peterson Gorentstein-Zierler(PGZ)算法的原理和各自的实现途径,比较了这两种算法的优缺点,得出了它们的不同应用条件。采用高速硬件描述语言(VHDL)成功实现了PGZ算法,并得到了理想的仿真结果。     

高级在轨系统中的RS(255,223)译码器的设计

在差错控制域中RS(255,223)码是一种性能优异的线性分组循环码,具有很强的随机错误和突发错误的纠错能力.设计中运用FPGA技术,使用Verlog HDL硬件设计语言实现高级在轨系统(AOS)中的RS译码器,着重介绍了RS译码器中改进结构的关键方程求解算法(uiBM),与目前广泛使用的无逆Berlekamp-Mas...     

On decoding of both errors and erasures of a Reed-Solomon codeusing an inverse-free Berlekamp-Massey algorithm

In a previous article by Truong et al. (see ibid., vol.46, p.973-76, 1998), it was shown that an inverse-free Berlekamp-Massey (1968, 1969) algorithm can be generalized to find the error locator polynomial in a Reed-Solomon (RS) decoder for correcting errors as well as erasures. The basic idea of this procedure is the replacement of the initial condition of an inverse-free BM algorithm by the Forney (1965) syndromes. It is shown that the errata locator polynomial can be obtained directly by initializing an inverse-free BM algorithm with the erasure locator polynomial and the syndromes. An important ingredient of this new algorithm is a modified BM algorithm for computing the errata locator polynomial. As a consequence, the separate computation of the erasure locator polynomial and the Forney syndrome, needed in the decoder developed by Truong et al., are completely avoided in this modification of the BM algorithm. This modified algorithm requires fewer finite field addition and multiplication operations than the previous algorithm. Finally, the new decoding method was implemented on a computer using C++ language. It is shown in a simulation that the speed of this new decoder is faster than the decoder developed by Truong et al. An example using this program is given for an (255, 239) RS code for correcting errors and erasures with 2ν+s⩽10     

Inversionless decoding of both errors and erasures of Reed-Solomoncode

Previously, the authors proposed an inverse-free Berlekamp-Massey (1968, 1969) algorithm to simplify the Reed-Solomon (RS) codes. This modified RS decoding method is the best known technique for finding the error locator polynomial. The inverse-free method is generalized to find both errors and erasures. The basic idea of the new procedure is the replacement of the initial condition of the BM algorithm by the Forney (1965) syndromes. With this improved technique, the complexity of time-domain RS decoders for correcting both errors and erasures is reduced substantially from previous approaches     

Computation of random coding exponent functions

Gallager's exponent functionE_{circ}, (rho,p)plays a crucial role in the derivation of bounds for coding error probabilities. An iterative algorithm for computing the maximum ofE_{circ} (rho,p)over the set of input probability distributions is presented. The algorithm is similar to that of Arimoto and Blahut for computing channel capacity. It is shown that the approximation error is at most inversely proportional to the number of iterations. A similar iterative algorithm for computing the source code reliability-rate function also is presented.