一类特殊码长的非对称量子BCH码

非对称量子纠错码是针对量子通信中不同类型量子错误发生的概率而设计的有效编码方案.纠错性能良好的量子码在量子通信的真实性和可靠性方面起着决定性的作用.本文首先通过研究分圆陪集的性质确定出非本原狭义BCH码满足Hermitian对偶包含的条件;其次,利用推广的CSS构造法构造出一系列特殊码长的非对称量子BCH码;最后,给出了m分别为3和5的两类非对称量子BCH码维数,它们的z-距离远大于已有文献中的结论,因而提高了非对称量子信道中对相位错误的纠错能力.     

Generalized Union Bound for Space–Time Codes

Gallager's second bounding technique, also known as the generalized union bound, is employed to derive a new upper bound on the error probability of space-time codes (STCs) with maximum-likelihood (ML) decoding on quasi-static Rayleigh fading channels. The new bound is distinguished by two characteristics: unlike the classical union bound, the new bound is rapidly convergent and is only a few decibels away from simulation results; and compared with Gallager's first bound, it has better computational efficiency and numerical stability. Hence, the new bound is a useful tool for performance analysis and computer search of good STCs. Moreover, the correlation between fading coefficients is easily accommodated by the new bound. The application of the new bound to convolutional coding on block-fading channels is also demonstrated, and an improved version is derived for the bit-error probability of maximum a posteriori probability decoding     

Note on a Class of Codes Introduced by Séguin, Allard, and Bhargava

In this correspondence, we apply a theorem in finite geometry to obtain an improvement of the codes recently introduced by Séguin, Allard, and Bhargava to provide error protection for data in the ASCII format. Our construction yields a fast decoding algorithm.     

广义TMR码的设计

本文推导了确定广义ＴＭＲ码截短距离ｄ（ｃ｜１）的一种算法，从而提供了字节长为任意的广义ＴＭＲ码的通用设计方法。     

几何广义RS码的译码

本文给出了几何广义ＲＳ码的一种有效译码算法，该算法可对任意错误个数不超过「（ｄ－１）／２」的接收码字进行译码，其复杂度仅为Ｏ（ｎ＾３）。     

一类分裂的Caresian认证码的构造

利用Γ_a几何,构造了一类分裂的Cartesian认证码。     

新的非对称量子纠错码的构造

量子纠错码在量子通信和量子计算中起着非常重要的作用,之前的量子纠错码的构造大部分都集中在对称的量子信道,即量子比特翻转的错误概率与量子相位翻转的错误概率相等。该文在非对称量子信道上,即量子比特翻转的错误概率小于量子相位翻转的错误概率,利用经典的平方剩余码和Reed-Muller码构造一批非对称的量子纠错码。同已知的非对称量子纠错码的构造方法相比,该构造方法简单。并且,利用有限域的扩域到其子域的迹映射,构造得到了更多的非对称量子纠错码。     

Braided Convolutional Codes: A New Class of Turbo-Like Codes

We present a new class of iteratively decodable turbo-like codes, called braided convolutional codes. Constructions and encoding procedures for tightly and sparsely braided convolutional codes are introduced. Sparsely braided codes exhibit good convergence behavior with iterative decoding, and a statistical analysis using Markov permutors shows that the free distance of these codes grows linearly with constraint length, i.e., they are asymptotically good.     

Laminated Turbo Codes: A New Class of Block-Convolutional Codes

In this paper, a new class of codes is presented that features a block-convolutional structure-namely, laminated turbo codes. It allows combining the advantages of both a convolutional encoder memory and a block permutor, thus allowing a block-oriented decoding method. Structural properties of laminated turbo codes are analyzed and upper and lower bounds on free distance are obtained. It is then shown that the performance of laminated turbo codes compares favorably with that of turbo codes. Finally, we show that laminated turbo codes provide high rate flexibility without suffering any significant performance degradation.     

环Z2m上一类常循环码的挠码及其应用

该文研究了环Z_2^m上任意长的（1+2λ）-常循环码的挠码及其应用.首先,给出环Z_2^m上（1+2λ）-常循环码的挠码.然后,利用挠码得到环Z_2^m上某些（1+2λ）-常循环码的齐次距离分布.同时,利用挠码证明了环Z_2^m上（2^m－1－1）-常循环自对偶码都是类型I码,并利用这类码构造了极优的类型I码.     

Cyclic Codes and Sequences From Generalized Coulter–Matthews Function

In this paper, we will study the exponential sum $sum_{xin {BBF}_q}chi(alpha x^{(p^k+1)/2}+beta x)$ that is related to the generalized Coulter–Matthews function $x^{(p^k+1)/2}$ with $k/{rm gcd}(m,k)$ odd. As applications, we obtain the following: the correlation distribution of a $p$-ary $m$-sequence and a decimated $m$-sequence of degree ${p^k+1 over 2}$;      

Efficient Generalized Minimum-distance Decoders of Reed-Solomon Codes

Generalized minimum distance (GMD) decoding of Reed–Solomon (RS) codes can correct more errors than conventional hard-decision decoding by running error-and-erasure decoding multiple times for different erasure patterns. The latency of the GMD decoding can be reduced by the Kötter’s one-pass decoding scheme. This scheme first carries out an error-only hard-decision decoding. Then all pairs of error-erasure locators and evaluators are derived iteratively in one run based on the result of the error-only decoding. In this paper, a more efficient interpolation-based one-pass GMD decoding scheme is studied. Applying the re-encoding and coordinate transformation, the result of erasure-only decoding can be directly derived. Then the locator and evaluator pairs for other erasure patterns are generated iteratively by applying interpolation. A simplified polynomial selection scheme is proposed to pass only one pair of locator and evaluator to successive decoding steps and a low-complexity parallel Chien search architecture is developed to implement this selection scheme. With the proposed polynomial selection architecture, the interpolation can run at the full speed to greatly increase the throughput. After efficient architectures and effective optimizations are employed, a generalized hardware complexity analysis is provided for the proposed interpolation-based decoder. For a (255, 239) RS code, the high-speed interpolation-based one-pass GMD decoder can achieve 53% higher throughput than the Kötter’s decoder with slightly more hardware requirement. In terms of speed-over-area ratio, our design is 51% more efficient. In addition, compared to other soft-decision decoders, the high-speed interpolation-based GMD decoder can achieve better performance-complexity tradeoff.     

Using Reed–Muller RM (1, m) Codes Over Channels With Synchronization and Substitution Errors

We analyze the performance of a Reed-Muller RM(1,m) code over a channel that, in addition to substitution errors, permits either the repetition of a single bit or the deletion of a single bit; the latter feature is used to model synchronization errors. We first analyze the run-length structure of this code. We enumerate all pairs of codewords that can result in the same sequence after the deletion of a single bit, and propose a simple way to prune the code by dropping one information bit such that the resulting linear subcode has good post-deletion and post-repetition minimum distance. A bounded distance decoding algorithm is provided for the use of this pruned code over the channel. This algorithm has the same order of complexity as the usual fast Hadamard transform based decoder for the RM(1,m) code     

一类四重和六重线性码的构造

低重线性码在结合方案、认证码以及秘密共享方案等方面有着极其重要的作用,因而低重线性码的设计一直是线性码的重要研究方向。该文通过选取恰当的定义集,构造了有限域${F_p}$(p为奇素数)上的一类四重和六重线性码,利用高斯和确定了码的重量分布,并编写Magma程序进行了验证。结果表明,构造的码中存在关于Singleton界的几乎最佳码。     

一种新型的准正交空时分组码设计

本文提出了一种新的准正交设计方案。用该方案构造准正交STBC是在基于最大速率设计的OSTBC的基础上引入了非正交设计,以2×2Almouti复子矩阵为构造单元,以牺牲正交性为代价换得速率的提高。为了尽可能减小引入非正交性带来的译码复杂度的增加,对2×2Almouti复子矩阵采用两种不同的形式,从而可以使得最小欧氏距离的联合译码算法简化成为部分基于成对码字和其余的基于单个码字译码。同时对基于这种准正交设计方案构造的STBC进行了性能仿真。     

一种高码率低复杂度准循环LDPC码设计研究

该文设计了一种特殊的高码率准循环低密度校验(QC-LDPC)码,其校验矩阵以单位矩阵的循环移位阵为基本单元,与随机构造的LDPC码相比可节省大量存储单元。利用该码校验矩阵的近似下三角特性,一种高效的递推编码方法被提出,它使得该码编码复杂度与码长成线性关系。另外,该文提出一种分析QC-LDPC码二分图中短长度环分布情况的方法,并且给出了相应的不含长为4环QC-LDPC码的构造方法。计算机仿真结果表明,新码不但编码简单,而且具有高纠错能力、低误码平层。     

一种非规则广义LDPC码的构造方法

广义低密度奇偶校验(Generalized Low睤ensity Parity睠heck,GLDPC)码把低密度奇偶校验(Low睤ensity Parity睠heck,LDPC)码中的单奇偶校验(Single Parity睠heck,SPC)节点替换为校验能力更强的广义约束(Generalized Constraint,GC)节点,使其在中短码和低码率的条件下具有更低的误码率。传统GLDPC码要求基矩阵的行重等于分量码的码长,这限制了GLDPC码构造的灵活性。另外,相比于传统GLDPC码中GC节点位置的随机选取,GC节点的位置选择在GLDPC码的误码率性能上有一定的优化空间。针对以上两点,提出了一种基于渐进边增长(Progressive Edge-rowth,PEG)算法的非规则GLDPC码构造方法和一种基于Tanner图边数的GC节点位置选择算法。使用PEG算法生成的非规则LDPC码作为本地码,根据本地码的校验节点度使用多种分量码,结合GC节点位置选择算法构造非规则GLDPC码。仿真结果表明,与传统方法构造的GLDPC码相比,基于Tanner图边数的GC节点位置选择算法构造的非规则PEG-LDPC码在误码率和译码复杂度上均得到明显改善。     

视频字符叠加器

文章介绍了实现在电视信号上叠加字符的方法，并具体给出了一个实际用于水井电视检修的视频字符叠加器的软硬件。