Golay码的快速译码

本文利用Ｇｏｌａｙ码的代数结构给出了二元（２３，１２，７）Ｇｏｌａｙ码及三元（１１，６，５）Ｇｏｌａｙ码新的译码算法。对于二元Ｇｏｌａｙ码，所提的算法的最坏时间复杂性为５３４次ｍｏｄ２加法，比已知的同类译码算法的时间复杂性都小；平均时间复杂性为２２４次ｍｏｄ２加法，比目前已知的最快的译码算法的平均时间复杂性２７９次ｍｏｄ２加法还要小。对于三元Ｇｏｌａｙ码，所提算法的最坏时间复杂性为１２３次ｍｏｄ３加法，平均时间复杂性为８５次ｍｏｄ３加法，比同类的算法都快。此外，这里给出的算法结构简单，易于实现。     

一类三元线性分组码的译码

Ｐｌｅｓｓ［１］证明了三元（１２，６，６）Ｇｏｌａｙ码具有一种双层结构，并据此给出了该码的快速硬判决译码算法。本文推广了Ｇｏｌａｙ码的Ｐｌｅｓｓ结构，给出了由三元（ｎ，ｋ，ｄ）线性分组码构造的三元（３，ｎ＋ｋ，≥ｍｉｎ（ｎ，２ｄ，６））线性分组码，其中包括（１２，６，６）Ｇｏｌａｙ码和（１８，９，６）码，并以三元（１８，９，６）码为例给出了这类码的最大似然软判决译码算法。     

神经网络在分组码软判决译码中的应用

本文对线性分组码构造了一个神经网络软判决译码器，并提出了循环码的一个神经网络软判决译码算法。对Ｇｏｌａｙ码的计算机仿真表明，新算法不仅译码速度快，而且，具有优越的性能。     

一种Golay码的快速译码算法

本文提出了一种（２４，１２，８）扩展Ｇｏｌａｙ码的新的软判决译码算法，其译一组码字的运算量最多为５０７次二元运算，优于目前已发表的各种算法。我们证明了该算法，并实现了广义最小距离译码。计算机模拟表明在完备译码时其性能与最大似然译码几乎一样。     

两类新的线性分组码的译码

本文推广了Ｐｌｅｓｓ由四元线性分组码构造Ｇｏｌａｙ码和由三元（４，２，３）线性分组码构造三元（１２，６，６）Ｇｏｌａｙ码的投影方法，给出了由四元（ｎ，ｋ，ｄ）线性分组码构造的二元（４ｎ，ｎ＋２ｋ，≥ｍｉｎ（８，ｎ，２ｄ）线性分组码和由三元（ｎ，ｋ，ｄ）线性分组码构造的三元（３ｎ，ｎ＋ｋ，≥ｍｉｎ（ｎ，２ｄ，６）线性分组码，并根据所得码的结构给出了有效的最大似然译码算法。     

基于FIA的代数几何码的译码

设Ｃ是亏格为ｇ的不可约代数曲线；Ｃ（Ｄ，Ｇ）为Ｃ上的代数几何码，该码的设计距离为ｄ＝ｄｅｇ（Ｇ）－２ｇ＋２。本文首先从理论上证明所给算法的合理性，然后给出一种基于基本累次算法（ＦＩＡ）的译码算法。该算法是Ｇ．Ｌ．Ｆｅｎｇ等人（１９９３）提出的算法的改进。它可对≤〔（ｄ－１）／２〕个错误的接收向量进行译码。运算量与存贮量约为Ｇ．Ｌ．Ｆｅｎｇ等人算法的一半，且便于软硬件实现。     

纠错编码在无线寻呼系统中的应用

本文系统探讨了纠错编码在无线寻呼系统中应用的主要纠错性能错误。主要是Ｇｏｌａｙ（２３，１２）码、ＢＣＨ（３１，１６）码，“ＰＯＳＡＧ”码、Ｋａｓａｍｉ（２６，１６）缩短码和ＦＬＥＸ码，并比较了它们的主要性能指标，这对于如何选用无线寻呼系统中的纠错码有重要的参考价值。     

增加捕错窗口长度的译码法

当不是ｇ（ｘ）的因子，ｇ（ｘ）和ａ（ｘ）ｇ（ｘ）分别是二元线性循环码Ｃ（ｘ）和Ｃｓｕｂ（ｘ）的生成多项式时，则Ｃｓｕｂ（ｘ）是Ｃ（ｘ）的子码。恰当选用Ｃ（ｘ）／Ｃｓｕｂ（ｘ）的２ｊ个余式将Ｃ（ｘ）转换为子码，然后对子码捕错；当错误矢量Ｅ（ｘ）的重量Ｗ（Ｅ）ｔ，且有连续ｋ－ｊ位为零时，就能正确译码。该法提高了纠错能力，还可分类译码输出，结构简单，实现容易。     

基于定点DSP的Turbo码译码器实现

在介绍了一种改进的Max—Log-MAP译码算法基础上．讨论了与定点DSP实现译码算法相关的量化精度、溢出处理及数据存储等几个问题，并采用VC5409实现了（13．15）8Turbo码译码器．经测试．其性能接近浮点译码性能．     

一类缩短Fire码的快速译码

Fire码是很重要的一类纠正单个突发错误的循环码。在实际中广泛应用的是缩短Fire码,因此研究缩短Fire码的快速译码方法非常重要。GSM的大部分逻辑控制信道和GPRS中的编码策略CS-1使用的便是一种缩短Fire码。本文先回顾了Fire码和缩短Fire码的概念,并提出了一种快速译码的方法。接下来,针对GSM与GPRS中的缩短Fire码,提出了具体的实现方案。     

Concatenated coding with inner trellis codes for fading channels

It is known that concatenated coding can significantly enhance the performance of digital communication systems operating over fading channels when compared to uncoded or single-coded systems. The price to be paid for such an improvement, however, is a substantial increase in the required bandwidth. In this paper, we consider the use of a concatenation scheme in which the inner code is a trellis-coded modulation (TCM) system. The analysis is carried out for two different outer codes: a binary Golay code and a non-binary Reed-Solomon code. Results obtained for the Rayleigh and Rician fading channels through analytical bounds indicate that the use of this system does provide a significant reduction in the bit error probability, a fact that is also verified through computer simulation. Unlike a traditional concatenated system, the proposed method achieves the coding gain while maintaining acceptable bandwidth efficiency.     

环F2+uF2+…+uk-1F2上常循环自对偶码

最近,剩余类环上的常循环码及常循环自对偶码引起了编码学者的极大关注.本文首先利用一些相关的线性码,建立了一类特殊有限链环上长为N的常循环自对偶码的一般理论,利用其结果给出了该环上长为N的(1+uλ)-常循环自对偶码存在的充分条件,得到了该环上长为N的一些常循环自对偶码,并给出了其生成多项式.     

New simple encoder and trellis decoder for Golay codes

New simple encoding and trellis decoding techniques for Golay codes, based on generalised array codes (GAGs) are proposed. The techniques allow the design of both (23,12,7) Golay and (24,12,8) extended Golay codes with minimal trellises. It is shown that these trellises differ only in the last trellis depth with different labelling digits.<>     

DNA Golay码的设计与分析

 DNA编码是DNA计算初始数据库中寡核苷酸序列的设计问题.合理的DNA编码可以提高实验的稳定性和正确性,从而确保DNA计算的成功率.本文给出DNA码字重量和DNA码字间Watson-Crick Hamming距离的定义;提出DNA Golay码的设计方法;分析了DNA Golay码的性质和规模;与随机搜索优码方法相比,DNA Golay码求解优码更加简单可行.     

Generalized Reed-Muller codes and power control in OFDM modulation

Controlling the peak-to-mean envelope power ratio (PMEPR) of orthogonal frequency-division multiplexed (OFDM) transmissions is a notoriously difficult problem, though one which is of vital importance for the practical application of OFDM in low-cost applications. The utility of Golay complementary sequences in solving this problem has been recognized for some time. In this paper, a powerful theory linking Golay complementary sets of polyphase sequences and Reed-Muller codes is developed. Our main result shows that any second-order coset of a q-ary generalization of the first order Reed-Muller code can be partitioned into Golay complementary sets whose size depends only on a single parameter that is easily computed from a graph associated with the coset. As a first consequence, recent results of Davis and Jedwab (see Electron. Lett., vol.33, p.267-8, 1997) on Golay pairs, as well as earlier constructions of Golay (1949, 1951, 1961), Budisin (1990) and Sivaswamy (1978) are shown to arise as special cases of a unified theory for Golay complementary sets. As a second consequence, the main result directly yields bounds on the PMEPRs of codes formed from selected cosets of the generalized first order Reed-Muller code. These codes enjoy efficient encoding, good error-correcting capability, and tightly controlled PMEPR, and significantly extend the range of coding options for applications of OFDM using small numbers of carriers     

Linear codes with Pless structures

Extended Golay codes possess certain two-level structures which are important for decoding the codes. However, these ideal structures are not limited to Golay codes. Here, the structures are generalised to other linear codes. Among which are a binary (20. 9, 7) code, a binary (32, 16, 8) code, a binary (40, 20, 8) code and a ternary (18, 9, 6) code. Similar to the Golay codes, there are also efficient decoding algorithms for these codes, which are sufficiently simple to enable decoding the derived codes by hand calculations     

在BIAWGN信道下规则LDPC码的设计与仿真分析

LDPC码是一种逼近香农限 ,实现容易 ,系统复杂度低的优秀的线性纠错码。奇偶校验矩阵 H是决定一个 LDPC码性能的关键。本文针对规则 LDPC码 ,提出了两种随机构造 H的方式 :行列都均匀的 evenboth和仅列均匀的 evencol。通过仿真分析发现 ,由 evenboth方式生成的规则 LDPC码性能更好。本文还对规则 LDPC码与卷积码的性能进行了对比 ,证明了规则 LDPC码在中短帧传输下的优异性能。这对 LDPC码投入实际应用具有重要的意义     

ALE控制器编解码技术及其DSP实现

ALE控制器是短波自适应通信系统的核心部件,它采用G o lay码和交织码来提高数据传输的可靠性。G o lay码是一种广泛应用的能纠多个错误的完备码,交织码则是一种特别适合于抗突发错误通信的码。本文阐述了ALE控制器中采用的G o lay(24,12)编解码和交织编解码的关键技术及其在TM S320C 33上的实现。     

A property of decomposable Golay codes which greatly simplifies sidelobe calculation

Pure-sense complementary sequences are an important class of codes that were invented by Golay. With but two non-trivial exceptions, Golay codes of all known lengths are, or can be, made to be decomposable; that is, they can be considered to be formed from the apposition of two equal-length subcodes. Hence the technique in this letter applies to Golay codes of most known lengths. The value of the property is that it reduces the labor of computation of the autocorrelation function sidelobes of the Golay codes by a factor of at least two. Furthermore, it is applicable to either marine or manual calculation. It also provides another way of analyzing auto-correlation functions in general.     

A decoding procedure for multiple-error-correcting cyclic codes

A decoding procedure for multiple-error-correcting cyclic codes is described. This method is very simple in principle and the mechanization is easy for short codes with relatively high redundancy. Applications are made to the cyclic Golay code, the Bose-Chaudhuri(63, 45), (31, 16), (31, 11)codes and the(41, 21)cyclic codes. A block diagram for a decoder for the Golay code is shown.