应用于片上网络的BCH码的设计与实现

本文对差错控制编码技术在片上网络(NoC)中的应用进行了研究。通过对三种纠错码在纠错能力、码率、面积和功耗等方面的折中,本文设计实现了适用于片上网络通信的BCH码,并给出了仿真结果。最后将BCH码应用在Hermes NoC平台上,成功地实现了一个基于BCH码的交换—交换的NoC差错控制系统。     

有限域上非本原BCH码的对偶包含判定

 循环陪集在经典和量子纠错编码理论中具有非常重要的作用.根据CSS编码定理知,利用经典BCH码构造量子BCH码时需要判断经典BCH码是否包含其对偶码.本文给出了循环陪集的若干重要性质,根据这些性质得到了判断有限域上非本原BCH码是否包含其对偶码的准则.本文给出的判断准则时间复杂度为多项式的,并且该判断准则对本原BCH码也适用.     

基于FPGA的BCH编码器的设计

BCH码是一种获得广泛应用的能够纠正多个错码的循环码。介绍了BCH编码原理,基于FPGA,利用VHDL硬件描述语言实现了一个BCH(15,11)码编码器。给出了仿真结果。仿真结果表明,达到了预期的设计要求,并用于实际项目中。     

一种基于FPGA的纠错编译码器的设计与实现

在信道容量以内,香农论证可通过对信息的恰当编码,由信道噪声引入的错误可以被控制在任何误差范围之内.丈章通过对无线信道中纠错编码的研究,提出一种BCH码的简单编译码设计思想和方法,应用Altera公司开发的硬件描述语言VHDL及开发系统软件QuartusⅡ,实现了基于FPGA(现场可编程门阵列)的BCH(31,21,2)码编、译码全数字过程,并给出了仿真波形,证实了此种编译码器的可实现性.     

DTMB标准BCH译码器设计

BCH码是目前最为常用的纠错码之一,我国的数字电视广播地面传输标准DTMB也使用了缩短的BCH码作为前向纠错编码的外码。针对该BCH码的特点,采用BM译码算法,设计了一种实时译码器。与其它设计方案相比较,显著减少了占用逻辑数量。整个设计在Stratix II FPGA上进行了综合验证,满足了设计要求。     

两类厄米特对偶包含的BCH码及其应用

Bose-Chaudhuri-Hocquenghem(BCH)码是一类重要的经典纠错码,可以纠正多个错误且具有高效的编码和译码方法,满足一定结构关系的BCH码可以构造量子纠错码.本文研究了有限域上两类BCH码,基于分圆陪集的结构性质,给出了这两类BCH码满足厄米特对偶包含的条件,通过确定每个分圆陪集所含元素个数,计算出了这两类厄米特对偶包含的BCH码的维数,并利用厄米特构造法,由这两类厄米特对偶包含的BCH码得到了一些参数较好的量子纠错码.     

基于概率逼近的本原BCH码编码参数的盲识别方法

针对本原BCH码编码参数的盲识别问题,该文提出了一种基于概率逼近的盲识别方法。首先,利用Gauss分布和Poisson分布逼近随机码字的根概率特性,确定了搜索BCH码长的门限;然后,通过分析本原域元素的检错能力及同构对域的影响,应用临近域对的方法确定编码域,提高了其识别能力;最后,给出识别生成多项式时的共轭根系表,从而减少了计算量。仿真结果表明,在较高的误码率下,该方法能快速地识别出BCH码编码所采用的编码参数。     

短波极低信噪比条件下的数传编码交织技术

从工程观点研究了极低信噪比条件下的数据传输技术，给出了一种BCH码的编码、译码结合交织技术的方案，并在DSP平台上实现，达到了系统抗突发差错干扰要求。     

关于q元BCH码的维数和最小距离

本文讨论的是q元狭义本原BCH码,以下简称BCH码。首先给出了一定条件下求BCH码维数的一般公式,该结果改进了MacWilliams等人(1977)的结果。然后给出了求BCH码维数的一般迭代方法。此外,本文还指出了BCH码的最小距离的BCH界是分圆陪集首,我们猜测BCH码的最小距离也是分圆陪集首。     

数字电视地面广播标准中准循环LDPC码的编码方法研究

在数字电视地面广播国家标准中的前向纠错编码（FEC）部分,采用BCH码和LDPC码进行级联的编码方案。本文给出了国家标准中准循环LDPC码的参考编码算法,探讨了该码对应的生成矩阵特点及编码步骤,编程实现了编译码算法,并进行了仿真,结果表明国标中的准循环LDPC码在AWGN信道中极低信噪比情况下仍具有较好的纠错性能。     

A Simple BCH Decoder for NoC Interconnects and SoC Buses

Network on a chip (NoC) uses packet-switched network to implement interconnections in System on chip (SoC). In SoC design, performance and energy efficiency are respectively the first and second priorities, and optimal on-chip communication should decrease the power consumption and area overhead. In this work, a simplified BCH codec is proposed for reliable communication in NoC and SoC. It performs BCH error corrections without Berlekamp's algorithm, only using reduced syndrome bits to determine error patterns. The error locations can be found by looking up tables, by which the possible errors are directly corrected. Only one matrix product and one ROM access are required in the BCH decoder. The proposed (20, 8, 2) and (31, 16, 3) decoders in the paper can be easily applied for error corrections of interconnects and buses for NoC and SoC. It is also beneficial to correct data lines without length definition and controllines without storage.     

Some Remarks on BCH Bounds and Minimum Weights of Binary Primitive BCH Codes

It is shown that ifm neq 8, 12andm > 6, there are some binary primitive BCH codes (BCH codes in a narrow sense) of length2^{m} - 1whose minimum weight is greater than the BCH bound. This gives a negative answer to the question posed by Peterson [1] of whether or not the BCH bound is always the actual minimum weight of a binary primitive BCH code. It is also shown that for any evenm geq 6, there are some binary cyclic codes of length2^{m} - 1that have more information digits than the primitive BCH codes of length2^{m} - 1with the same minimum weight.     

一种BCH码编译码器的设计与实现

二元BCH码具有良好的代数结构和纠错能力,是应用最为广泛的码类之一。在此介绍了BCH（255,223）的编译码算法和硬件实现方法,针对二元BCH码提出了一种适合硬件模块化设计的BM迭代译码算法,并基于Xilinx公司的xc5vlx110t实现了BCH（255,223）纠错编译码。仿真结果表明,采用此方法实现的编译码器具有速度快、构造简单、性能稳定以及结构灵活的优点。目前该编译码器已成功用于某数字电台系统中。     

On Quantum and Classical BCH Codes

Classical Bose-Chaudhuri-Hocquenghem (BCH) codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes; this correspondence studies the properties of such codes. It is shown that a BCH code of length n can contain its dual code only if its designed distance delta=O(radicn), and the converse is proved in the case of narrow-sense codes. Furthermore, the dimension of narrow-sense BCH codes with small design distance is completely determined, and - consequently - the bounds on their minimum distance are improved. These results make it possible to determine the parameters of quantum BCH codes in terms of their design parameters     

A simple decoding of BCH codes over GF(2m)

A simple decoding method for even minimum-distance Bose-Chaudhuri-Hochquenghem (BCH) codes is proposed. In the method the coefficients of an error locator polynomial are given as simple determinants (named Q determinants) composed of syndromes. The error evaluator is realized as a Q determinant divided by an error locator polynomial. The Q determinants can be efficiently obtained with very simple calculations on syndromes enabling the realization of a high-speed decoder of simple configuration. The number of calculations in obtaining the error locator and the error evaluator with the proposed method is smaller than that with the widely used Berlekamp-Massey algorithm when the number of correctable errors of the code is five or less. The proposed method can also be applied to the binary narrow-sense BCH codes of odd minimum distance     

New optimal partial unit memory codes based on extended BCH codes

Some new optimal binary partial unit memory codes are presented. The codes are constructed from extended BCH codes. A general method for constructing PUM codes based on extended RS and BCH codes is described.<>     

高速Berlekamp-Massey算法结构及电路实现

介绍了两种用于二进制BCH解码器的高速Berlekamp—Massey算法实现方案。在加入寄存器以减少关键路径的延时从而提高电路速度的基础上，一种方法是采用有限域乘法器复用的方法降低电路的复杂度；另一种方法则通过对有限域乘法器进行流水线设计，进一步提高电路的工作速度，实现超高速应用。设计中充分利用了二进制BCH码中Berlekamp—Massey算法迭代计算时修正值间隔为零的性质，用超前计算的方法减少了运算周期的增加。提出的方案可用于设计高速光通信系统的信号编解码芯片。     

Long primitive binary BCH codes have distanced leq 2n ln R^{-1}/log n cdots

In this paper, we obtain upper and lower bounds on the designed and actual distances of any sequence of extended primitive BCH codes of increasing lengthsnand fixed rateR. The results of this paper are based on [1, ch. 12], which gives an exact expression for the rates of any sequence of extended primitive BCH codes of increasing length and fixed ratio of distance/length.     

On the dimension and minimum distance of BCH codes over GF(q)

In this paper, only narrow-sense primitive BCH codes over GF(q) are considered. A formula, that can be used in many cases, is first presented for computing the dimension of BCH codes. It improves the result given by MacWilliams and Sloane in 1977. A new method for finding the dimension of all types of BCH codes is proposed. In second part, it is proved that the BCH bound is the leader of some cyclotomic coset, and we guess that the minimum distance for any BCH code is also the leader of some cyclotomic coset. Supported by the National Natural Science Foundation of China     

BCH编译码的DSP实现

介绍了信道编码中常用的BCH码的基本原理。讨论了TMS320C54X定点DSP芯片,结合CCS开发平台的特点,完成了以C语言为基础的BCH编译码的DSP实现。经测试,该软件设计在DSP硬件平台上运行良好,整个系统的各项性能指标均达到设计的要求。