BCH码分组交织参数盲识别

针对BCH码分组交织参数盲识别容错性能差和计算量大的问题,提出一种基于高斯列消元和深度谱相结合的BCH码分组交织参数盲识别方法。首先利用高斯列消元方法识别交织长度和同步参数,确定交织位置关系;其次根据交织位置关系得到码长后,然后利用深度谱识别生成矩阵,对生成矩阵进行高斯消元得到典型生成矩阵和生成多项式。该方法可以较好地识别BCH码分组交织的交织长度、同步参数、交织位置关系、BCH码码长及生成多项式。仿真实验表明,在误码率为 的情况下,对高码率BCH码分组交织的识别概率高于70%。     

秩距离BCH码的进一步研究

本文作者在“关于秩距离BCH码的校验矩阵及其秩距离”一文中提出了秩距离BCH码的概念，讨论了所给秩距离BCH码为最大秩距离BCH码时，码的生成多项式的根应满足的条件。本文在此基础上，讨论当线性秩距离码的生成多项式具有广义连续根时，它能构成秩距离BCH码的充分条件并给出了此充分条件。     

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.     

非理想同步下BCH码盲识别的改进算法

为实现信道差错概率未知和非理想同步条件下BCH码的盲识别,本文提出了一种改进的盲识别算法。首先,结合调制方式和信噪比估计算法估计出信道差错概率;然后,根据该信道差错概率推导出一个最佳判决界,以判断测试域指数下某个最小多项式是否为生成多项式的因式,完成码长的识别;最后,比较各测试同步偏差下全部行多项式中被最小多项式整除的个数识别出实际同步偏差,并找到满足判决界的全部最小多项式完成生成多项式的识别。仿真结果表明,在信道差错概率未知和非理想同步条件下,本文算法能够有效的完成对BCH码的识别,且识别性能优于已有算法。      

基于贪心算法构成的正交矩阵及保密通信

提出用贪心算法来构成全正交或类正交矩阵的方法。首先,建立模型,并对该模型进行仿真验证,统计对应列数r一定时的全正交或类正交矩阵数量,进而分析这些矩阵的性质,如唯一性、均衡性、行列正交性以及r变化时的矩阵数量。其次,在此基础上,对其在保密通信中的应用进行了分析和实现,从而说明这种矩阵在保密通信中的可行性和实用性,因其在大小上不受任何限制,数量上较相同列数的walsh矩阵多得多,为保密通信的提供更多的可用密钥序列。     

多维类正交伪随机矩阵多项式的组合特性研究

研究用于产生多维类正交伪随机矩阵的生成多项式,这既可以由同组的多项式按照顺序的方式组合而成,也可以由不同阶的多项式按照任意的顺序组合而成,同时还可以由多项式的逆组合而成。由不同方法组合而成的生成多项式,经过群变换和数值转换之后得到的多维类正交伪随机矩阵也不同。所以,生成多项式组合方法的多样化,也使其对应产生的多维类正交伪随机矩阵更为丰富,从而得到更多的能应用于码分多址（Code division multiple access,CDMA）等通信系统中的类正交序列。     

关于秩距离BCH码的校验矩阵及其秩距离

本文基于秩距离码提出了秩距离BCH码,给出了其校验矩阵的形式,并讨论了所给秩距离BCH码为最大秩距离HCH码时,码的生成多项式的根应满足的条件。     

关于零相关窗互补码理论界的几点讨论

提出了一类新型的零相关窗互补码，这类新型零相关窗互补码可以表示为三个独立的元素：一对相互正交的互补码、一个正交矩阵和一个标号矩阵的组合。本文重点讨论了这类新型零相关窗互补码的副峰平方之和的理论界，证明了几个重要的定理。这些定理包括：副峰的平方之和只是相对偏移的函数、零相关窗互补码集的一致性、列旋转不变性及列排列不变性等。这些定理对零相关窗互补码的设计具有重要的指导意义。     

基于循环长除法的BCH(31,16)译码算法

BCH码的快速译码算法一直是纠错编码领域研究的一个热点问题,针对特殊的BCH(31,16)快速译码问题,提出了一种新颖的基于循环长除法和置换群理论相结合的译码算法。该算法首先利用有限域F 2(x)中的循环长除法,用接收到的含有错误位的接收码循环长除生成多项式得到余式,如果余式项数小于等于BCH(31,16)纠错范围,此余式即为错误多项式,和接收码模2相加即得原码。如果所得余式不满足上述要求,利用置换群理论对接收码进行位置置换,再循环长除生成多项式得余式,若此余式项数小于等于BCH(31,16)纠错范围,此余式即为错误多项式,逆置换此余式,和接收码模2相加即得原码。本算法和常规的BCH译码相比较,不需要存储错误图样,也不需要解BM方程,可直接可编程实现。理论分析和程序仿真均证明此算法有效可行,软硬件实现简单,具有重要的实际应用价值。     

BCH码对自由空间OCDMA系统性能的改善

基于自由空间的信道特性,提出用BCH信道编码来改善自由空间OCDMA系统性能.考虑系统中存在多用户干扰、背景光噪声以及APD接收机噪声的情况下,分析了基于多波长二维光正交码的同步OCDMA系统BCH编码前后的误码率公式,并对采用不同BCH码的系统误码率性能进行了计算机仿真.仿真结果表明,BCH码在降低系统编解码器的复杂度的同时能够有效地增加系统同时容纳的用户数,有效地降低系统对接收光功率的要求.     

二进制BCH码的一种盲识别方法

提出二进制BCH码的一种盲识别方法。该算法适用于本原和非本原二进制BCH码。首先,在帧长度已知的条件下,根据循环特性,给出一种分组长度的统计识别方法;然后,根据循环特性及各种约束条件得到备选多项式;再根据校正子权重和最小原则,得到最优多项式;最后通过因式分解得到生成多项式的最终估计表达式。仿真表明,本文算法具有较强的抗随机误码能力,而且其识别性能随着参加统计的码字数增多而提高。该算法不涉及矩阵运算,因此非常适合硬件实现。     

Group Codes and Walsh Functions

The set of Walsh functions, wal(j,?), is the character group of the dyadic group. For O?j?2k it is shown that they may also be derived from the character table of the abstract Abelian group Ck generated by k elements of order two. The method uses Slepians modular representation table[3] to compute the 2k irreducible representations (each of degree one) of Ck. The character table, K, is a 2kx2k square array of +1's and -l's and, considered as a matrix, the orthogonality relationships for characters show that K has the Hadamard property, [K][K]T = 2K [I]. In fact, for the proper ordering of the group elements in the construction of the modular representation table it is the Hadamard matrix, the entries of whose ith row take on the values of the Walsh function wal (i,?) in each of ?/2k subintervals. In a similar way other permutations of the modular representation table define different functions taking on the values +l, -l, also orthogonal and in a one to one relationship to the Walsh functions. Since an n place binary group code with k information places is isomorphic to Ck,[3] each code can thus be used to generate real functions orthogonal over a given interval or period ?. In the special case of cyclic codes where the elements of the code interpreted as polynomials form an ideal in a polynomial ring of characteristic two, the group operation used in deriving the character table is of course, addition.     

Decoding binary two-error correcting cyclic codes with Zechlogarithms

A decoding method for binary two-error correcting cyclic codes whose generator polynomials have at most two irreducible factors is presented. This class includes binary narrow-sense BCH codes with designed distance 5. The decoding algorithm uses the Zech logarithm for the finite field in which the roots of the code lie     

Blind recognition of primitive BCH code based on average cosine conformity

In order to overcome the poor performance of existing algorithms for recognition of BCH code in low signal-to-noise ratio (SNR),a recognition algorithm based on average cosine conformity was proposed.Firstly,by traversing the possible values of code length and m-level primitive polynomial fields,the code length was identified by matching the initial code roots.Secondly,on the premise of recognizing the code length,the GF(2^m) domain was traversed under the m-level primitive polynomial and the primitive polynomial with the strongest error-correcting ability was the generator polynomial for the domain.Finally,the minimum common multiple corresponding to the minimum polynomial of code roots was obtained,and the BCH code generator polynomial was recognized.In checking matching,the statistic of average cosine conformity was introduced.The optimal threshold was solved based on the minimum error decision criterion and distribution of the statistic to realize the fast identification of the BCH.The simulation results show that the deduced statistical characteristics are consistent with the actual situation,and the proposed algorithm can achieve reliable recognition under SNR of 5 dB and code length of 511.Comparing with existing algorithms,the performance of the proposed algorithm is better than that of the existing soft-decision algorithm and 1~3.5 dB better than that of the hard-decision algorithms.     

最大公约式阶数分布的BCH码参数识别

针对BCH码的编码盲识别,在码字同步点已知的条件下,根据实际序列与随机序列最大公约式阶数分布(简记为GOD)之间的差异性特征,提出了一种运用两种量化指标(方差差值、平均欧氏距离)分别对码长进行识别的方法,通过比较这两种量化指标识别码长的容错性,进而提出一种新的融合指标的GOD识别码长方法。在此基础上,通过BCH码的特性,计算阶数分布差值,识别生成多项式,实现了BCH码的盲识别。GOD识别方法简单易行,理论分析及仿真实验表明该方法的容错性较强,融合指标的GOD识别码长方法在误码率为0.02条件下,对中短码识别效果达90%以上;误码率为0.005条件下,对中偏长码识别效果达90%以上。     

Some long cyclic linear binary codes are not so bad

We show that when an inner linear cyclic binary code which has an irreducible check polynomial is concatenated with an appropriately chosen maximal-distance-separable outer code, then the overall code is cyclic OverGF(2). Using this theorem, we construct a number of linear cyclic binary codes which are better than any previously known. In particular, by taking the inner code to be a quadratic residue code, we obtain linear cyclic binary codes of lengthN, rateR, and distanceD geq (1 - 2R)N/ sqrt{2 log N}, which compares favorably with the BCH distanceD sim (2 ln R^{-1})N/log N, although it still fails to achieve the linear growth of distance with block length which is possible with noncyclic linear concatenated codes. While this construction yields many codes, including several with block lengths greater than10^{10^5}, we have not been able to prove that there are arbitrarily long codes of this type without invoking the Riemann hypothesis or the revised Artin conjecture, as the existence of long codes of our type is equivalent to the existence of large primespfor which the index of 2 is(p - 1)/2.     

Studying the locator polynomials of minimum weight codewords of BCHcodes

Primitive binary cyclic codes of length n=2^m are considered. A BCH code with designed distance δ is denoted B(n,δ). A BCH code is always a narrow-sense BCH code. A codeword is identified with its locator polynomial, whose coefficients are the symmetric functions of the locators. The definition of the code by its zeros-set involves some properties for the power sums of the locators. Moreover, the symmetric functions and the power sums of the locators are related to Newton's identities. An algebraic point of view is presented in order to prove or disprove the existence of words of a given weight in a code. The principal result is the true minimum distance of some BCH codes of length 255 and 511. which were not known. The minimum weight codewords of the codes B(n2^h -1) are studied. It is proved that the set of the minimum weight codewords of the BCH code B(n,2^m-2-1) equals the set of the minimum weight codewords of the punctured Reed-Muller code of length n and order 2, for any m