一种基于极化码APC-SCL的译码算法

极化码在CRC-SCL译码方面需要逐层判决逐比特取值的比特依赖,是整个译码系统复杂度与延迟的主要来源.所以,本文在CRC-SCL译码的基础上提出一种新型的译码算法,即APC-SCL译码算法,并通过理论分析和MATLAB仿真,验证了在码长为1 024情况下译码的性能,在列表长度相同的条件下,APC-SCL译码算法相比CRC-SCL译码平均搜索宽度减少了26.5%,降低了系统复杂度,该算法在低信噪比区间效果更加明显.     

高性能LDPC/Turbo码双模译码器的发展综述

目前LDPC码和Turbo码广泛应用于3G和4G商用移动通信系统中,并且在无线局域网、光纤通信、水下通信、视频和图象的加密以及网络安全等方面也发挥着重要的作用.由于全球在不同地区的移动通信设备只支持一种码,这使得移动通信有一定的地域局限性并影响通信质量.因此,通过对LDPC码和Turbo码译码过程的研究与结合,实现一种高性能的LDPC/Turbo码双模译码器具有重要意义.文章回顾了目前LDPC/Turbo码双模译码器的发展情况,并针对存在的不足进行分析和总结,最后介绍LDPC码和极化码未来发展的趋势.     

极化码在OFDM水声通信中的应用研究

极化码(Polar code)因其高可靠性、实用的线性编、译码复杂度和理论上唯一可达香农极限等特点,成为信道编码领域新的研究热点.其编、译码方法的研究扩展至多种信道类型和应用领域,但在水声信道中的理论证明和应用研究相对较少且滞后.针对具有显著多途、多普勒扩散和有限带宽等复杂特性的水声信道,文章提出了与之相匹配的极化码信...     

基于协同优化算法的Reed-Solomon码迭代软判决译码

基于协同优化算法推导出一种Reed-Solomon(RS)码的迭代软判决译码(SDD)算法。该算法属于消息传递算法,具有严格的理论基础。仿真结果表明,该算法相对于硬判决译码(HDD)能够获得有效的软判决译码增益,对于(15,9)RS码在误帧率(FER)为4×10-4时有0.3~1.3dB的增益;同时译码复杂度低,具有很好的工程实用性。此外该算法是一类软输入软输出(SISO)译码算法,能够应用于以RS码为子码的复合码,如级连码和乘积码的迭代译码。     

低密度校验码量化译码研究

介绍了基于置信度传播算法的LDPC码和积译码算法，分析了译码中间变量的的密度进化特性，并对采用不同量化方案时LDPC码在AWGN信道下的译码性能进行了仿真研究。仿真结果表明相对连续译码．中间变量6bit均匀量化会带来约0．4dB左右的损失，而10bit非均匀量化性能明显得到改善。因此，合适的高阶量化译码可以获得接近连续译码的性能。     

基于k-Means算法的彩色QR码识别

为了降低彩色QR码解码过程中出现的混叠效应,提高彩色QR码解码的正确率,提出一种基于HSV颜色模型的k-Means聚类算法。为了选择适合彩色QR码的颜色空间模型,通过实验验证了在RGB,Lab,HSV 3个颜色模型下k-Means聚类算法的效果。在HSV颜色模型下,根据等欧氏距离的原则建立彩色编码模块的配色模型,最大程度地减小解码中颜色的混叠效应。彩色QR码解码预处理阶段,利用基于HSV颜色模型的光线补偿的k-Means聚类算法对彩色编码模块进行颜色分离,以提高解码的精度。研究结果表明:在HSV颜色模型下,k-Means聚类效果最好,图像区域分类效果最清晰;所建立的配色模型可以最优地为彩色编码模块配色;基于HSV颜色模型的光线补偿的k-Means聚类算法可以提高彩色QR码解码的正确率。因此,建立合理的配色模型进行彩色编码模块的颜色设置,同时采用基于HSV颜色模型的光线补偿的k-Means聚类算法进行颜色分割,可以大幅度地降低彩色QR码编码模块之间的混叠效应,从而显著提高彩色QR码解码的正确率。     

LT码的一种BP/ML混合译码算法

针对LT码在短信息字长度时采用置信传播(BP)译码和最大似然(ML)译码存在大的性能差异问题,提出了一种BP/ML混合译码算法来实现LT码在二进制删除信道(BEC)中译码复杂度和性能的合理折中.此算法在BP译码失败时只需运用ML译码确定少数猜测比特就可实现成功译码.仿真结果显示,相比于BP译码,BP/ML混合译码的译码...     

删除信道下LDPC码的优化设计算法

本文首先介绍了删除信道,及删除信道下LDPC码的优势,重点讨论了几种优化设计LDPC图的算法。其次,提出了一种限制环长加边算法,该算法比以往的优化算法有更小的复杂度和更好的性能。最后,对算法进行了仿真。     

分层空时码多载波CDMA的译码与检测

研究V－BLAST MIMO MC－CDMA下行系统。提出了一种对每个子载波进行V－BLAST译码的非线性 算法,对不同天线数、用户数情况进行了系统的仿真和分析,并对V－BLAST译码的线性和非线性算法进行了系 统仿真比较。     

基于RS算法的汉信码在金融票据系统中的应用研究

针对支票等金融票据在传递过程中的安全和智能化问题,介绍了一种基于Reed-Solomen(RS)算法的汉信码在金融票据中的应用系统。利用DSP高性能的专用数字信号处理芯片TMS320C5402,实现系统的数字控制,快速有效地完成数据编码;在分析RS纠错算法的基础上,利用Simulink仿真平台建立了RS编解码仿真模型图,并给出了相应的仿真结果,为分析与研究汉信码在金融票据系统中的应用提供理论依据。     

Two new decoding algorithms for Reed-Solomon codes

The subject of decoding Reed-Solomon codes is considered. By reformulating the Berlekamp and Welch key equation and introducing new versions of this key equation, two new decoding algorithms for Reed-Solomon codes will be presented. The two new decoding algorithms are significant for three reasons. Firstly the new equations and algorithms represent a novel approach to the extensively researched problem of decoding Reed-Solomon codes. Secondly the algorithms have algorithmic and implementation complexity comparable to existing decoding algorithms, and as such present a viable solution for decoding Reed-Solomon codes. Thirdly the new ideas presented suggest a direction for future research. The first algorithm uses the extended Euclidean algorithm and is very efficient for a systolic VLSI implementation. The second decoding algorithm presented is similar in nature to the original decoding algorithm of Peterson except that the syndromes do not need to be computed and the remainders are used directly. It has a regular structure and will be efficient for implementation only for correcting a small number of errors. A systolic design for computing the Lagrange interpolation of a polynomial, which is needed for the first decoding algorithm, is also presented.This research was supported by a grant from the Canadian Institute for Telecommunications Research under the NCE program of the Government of Canada     

基于比特可靠性的LDPC码编译码算法

提出了一种基于比特可靠性的低密度奇偶校验(LDPC)码编码算法和一种加权置信传播(BP)译码算法.该编码算法首先利用蒙特卡罗仿真得到LDPC码各个比特节点的出错概率,然后用已知信息替换易出错比特节点进行编码;该译码算法根据比特节点可靠性的差异,在译码时为每个比特节点赋予相应的权值,以调整它们对译码的影响程度.仿真表明,新的编译码算法使得系统性能大大提高,同时加快了译码迭代收敛速度.     

Modified sum-product algorithms for decoding low-density parity-check codes

The authors deal with the sum-product algorithm (SPA) based on the hyperbolic tangent (tanh) rule when it is applied for decoding low-density parity-check (LDPC) codes. Motivated by the finding that, because of the large number of multiplications required by the algorithm, an overflow in the decoder may occur, two novel modifications of the tanh function (and its inverse) are proposed. By means of computer simulations, both methods are evaluated using random-based LDPC codes with binary phase shift keying (BPSK) signals transmitted over the additive white Gaussian noise (AWGN) channel. It is shown that the proposed modifications improve the bit error rate (BER) performance up to 1 dB with respect to the conventional SPA. These results have also shown that the error floor is removed at BER lower than 10^-6. Furthermore, two novel approximations are presented to reduce the computational complexity of the tanh function (and its inverse), based on either a piecewise linear function or a quantisation table. It is shown that the proposed approximations can slightly improve the BER performance (up to 0.13 dB) in the former case, whereas small BER performance degradation is observed (<0.25 dB) in the latter case. In both cases, however, the decoding complexity is reduced significantly     

Construction and decoding of matrix-product codes from nested codes

We consider matrix-product codes ${[C_1\cdots C_s] \cdot A}$ , where ${C_1, \ldots , C_s}$ are nested linear codes and matrix A has full rank. We compute their minimum distance and provide a decoding algorithm when A is a non-singular by columns matrix. The decoding algorithm decodes up to half of the minimum distance.     

List decoding of repeated codes

Assuming that we have a soft-decision list decoding algorithm of a linear code, a new hard-decision list decoding algorithm of its repeated code is proposed in this article. Although repeated codes are not used for encoding data, due to their parameters, we show that they have a good performance with this algorithm. We compare, by computer simulations, our algorithm for the repeated code of a Reed–Solomon code against a decoding algorithm of a Reed–Solomon code. Finally, we estimate the decoding capability of the algorithm for Reed–Solomon codes and show that performance is somewhat better than our estimates.     

Gradient projection decoding of LDPC codes and algorithmic variations

The current study proposes decoding algorithms for low density parity check codes (LDPC), which offer competitive performance-complexity trade-offs relative to some of the most efficient existing decoding techniques. Unlike existing low-complexity algorithms, which are essentially reduced complexity variations of the classical belief propagation algorithm, starting point in the developed algorithms is the gradient projections (GP) decoding technique, proposed by Kasparis and Evans (2007). The first part of this paper is concerned with the GP algorithm itself, and specifically with determining bounds on the step-size parameter, over which convergence is guaranteed. Consequently, the GP algorithm is reformulated as a message passing routine on a Tanner graph and this new formulation allows development of new low-complexity decoding routines. Simulation evaluations, performed mainly for geometry-based LDPC constructions, show that the new variations achieve similar performances and complexities per iteration to the state-of-the-art algorithms. However, the developed algorithms offer the implementation advantages that the memory-storage requirement is significantly reduced, and also that the performance and convergence speed can be finely traded-off by tuning the step-size parameter.     

Fast decoding of non-binary first order Reed-Muller codes

A minimum distance decoding algorithm for non-binary first order Reed-Muller codes is described. Suggested decoding is based on a generalization of the fast Hadamard transform to the non-binary case. We also propose a fast decoding algorithm for non-binary first order Reed-Muller codes with complexity proportional to the length of the code. This algorithm provides decoding within the limits guaranteed by the minimum distance of the code.Partly supported by the Guastallo Fellowship. This work was presented in part at the 9th International Symposium Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, New Orleans, USA, October 1991     

Permutation decoding of codes from generalized Paley graphs

The generalized Paley graphs $\text{ GP }(q,k)$ GP ( q , k ) are a generalization of the well-known Paley graphs. Codes derived from the row span of adjacency and incidence matrices from Paley graphs have been studied in Ghinellie and Key (Adv Math Commun 5(1):93–108, 2011) and Key and Limbupasiriporn (Congr Numer 170:143–155, 2004). We examine the binary codes associated with the incidence designs of the generalized Paley graphs obtaining the code parameters $[\frac{qs}{2}, q-1, s]$ [ q s 2 , q - 1 , s ] or $[qs, q-1,2s]$ [ q s , q - 1 , 2 s ] where $s=\frac{q-1}{k}$ s = q - 1 k . By finding explicit PD-sets we show that these codes can be used for permutation decoding.