Hybrid Golomb codes for a group of quantised GG sources

The authors develop a class of codes for quantised generalised Gaussian (GG) sources. This new class of codes, that are called hybrid Golomb (HG) codes, are hybrids of Golomb-Rice (GR) codes and exp-Golomb (EG) codes. They integrate the properties of both GR and EG codes, which makes their performance more robust under variable source parameters. The efficiencies of the three classes of codes are compared and it is shown that the set of HG codes have efficiencies of approximately 70% or greater for a wide range of parameter values, whereas GR and EG codes can have efficiencies lower than 20%. The efficiencies of the set of HG codes are also compared with the set of EG codes that have the best performance under parameter scaling. It is shown that this set of HG codes still achieve a higher efficiency.     

Multifold Euclidean geometry codes

This paper presents a class of majority-logic decodable codes whose structure is based on the structural properties of Euclidean geometries (EG) and codes that are invariant under the affine group of permutations. This new class of codes contains the ordinary EG codes and some generalized EG codes as subclasses. One subclass of new codes is particularly interesting: they are the most efficient majority-logic decodable codes that have been constructed.     

On majority-logic decoding of finite geometry codes

In this paper, an improved decoding algorithm for codes that are constructed from finite geometries is introduced. The application of this decoding algorithm to Euclidean geometry (EG) and projective geometry (PG) codes is further discussed. It is shown that these codes can be orthogonalized in less than or equal to three steps. Thus, these codes are majority-logic decodable in no more than three steps. Our results greatly reduce the decoding complexity of EG and PG codes in most cases. They should make these codes very attractive for practical use in error-control systems.     

A novel construction of quantum ldpc codes based on cyclic classes of lines in euclidean geometries

The dual-containing (or self-orthogonal) formalism of Calderbank-Shor-Steane (CSS) codes provides a universal connection between a classical linear code and a Quantum Error-Correcting Code (QECC). We propose a novel class of quantum Low Density Parity Check (LDPC) codes constructed from cyclic classes of lines in Euclidean Geometry (EG). The corresponding constructed parity check matrix has quasi-cyclic structure that can be encoded flexibility, and satisfies the requirement of dual-containing quantum code. Taking the advantage of quasi-cyclic structure, we use a structured approach to construct Generalized Parity Check Matrix (GPCM). This new class of quantum codes has higher code rate, more sparse check matrix, and exactly one four-cycle in each pair of two rows. Experimental results show that the proposed quantum codes, such as EG(2,q)II-QECC, EG(3,q)II-QECC, have better performance than that of other methods based on EG, over the depolarizing channel and decoded with iterative decoding based on the sum-product decoding algorithm.     

Number of information symbols in polynomial codes

Polynomial codes and their dual codes as introduced by Kasami, Lin, and Peterson have considerable algebraic and geometric structure. It has been shown that these codes contain many well-known classes of cyclic codes as subclasses, such as BCH codes, projective geometry codes (PG codes), Euclidean geometry codes (EG codes), and generalized Reed-Muller codes (GRM codes). In this paper, combinatorial expressions for the number of information symbols and parity-check symbols in polynomial codes are derived. The results are applied to two important subclasses of codes, the PG codes and EG codes.     

Design of Quasi-Cyclic LDPC codes based on Euclidean Geometries

A new method for constructing Quasi-Cyclic (QC) Low-Density Parity-Check (LDPC) codes based on Euclidean Geometry (EG) is presented. The proposed method results in a class of QC-LDPC codes with girth of at least 6 and the designed codes perform very close to the Shannon limit with iterative decoding. Simulations show that the designed QC-LDPC codes have almost the same performance with the existing EG-LDPC codes.     

A note on one-step majority-logic decodable codes (Corresp.)

Construction of shortened geometric codes as Shown here results in 1-step majority-logic deeodable codes. The shortened codes retain the error-correction ability of the parent codes and the decoders for the shortened codes are much simpler than for the parent code. A table of shortened codes is given.     

基于欧氏几何的LDPC码构造方法

基于有限几何的低密度奇偶校验码(LDPC)是一种极具实用价值的码型。首先介绍了LD-PC码的原理和基本的构造方法,然后介绍了欧氏有限几何的概念,提出了一种构造欧氏有限几何LDPC码的方法,最后提出了对EG码字的改进方法。     

在CRC校验中提高码率的新方法

本文提出了扩展缩短码的新概念 ,研究了线性和非线性扩展缩短码的构造方法 ,对线性和非线性扩展缩短码的性能进行了理论分析 ,并通过 C+ +和 MATLAB相结合的仿真方法 ,分析了扩展缩短码的最小距离、码重分布、不可检错误概率等方面的性能 ,比较了扩展缩短码和原缩短码以及冗余分配方式不同的两种非线性扩展缩短码性能的优劣。结果表明 :扩展缩短码的理论是原 CRC码理论的完善和补充。本研究为 GSM系统提出了一种新的选择方法。在某些要求码率较高但冗余度不变的通信设备中 ,扩展缩短码是较好的选择     

A novel turbo coding scheme for satellite ATM using Reed-Muller codes

Block turbo codes with trellis-based decoding are proposed for use in cell-based satellite communication. Shortened Reed-Muller (RM) codes are used as the component codes because their minimal trellis is known. Simulation results for RM turbo codes and shortened RM turbo codes are presented over additive white Gaussian noise and Rayleigh fading channels. The performance of the shortened codes with different shortening patterns are shown. In some cases, the codes have the unequal error protection property, useful in asynchronous transfer mode cell formatting. In order to test the suitability of the proposed coding scheme from a practical point of view, the effect of channel impairments, including channel signal-to-noise ratio mismatch and carrier phase offset, are investigated.     

Optimum shortened cyclic codes for burst-error correction

This paper is concerned with the construction of the most efficient shortened cyclic (pseudo-cyclic) codes that can correct every burst-error of lengthbor less. These codes have the maximum number of information digitskamong all shortened cyclic burst-bcodes with a given number of check digitsr. The search procedure described is readily programmable for computer execution and efficient particularly for the case whereris close to the theoretical minimum of2bcheck digits. For2 leq b leq 10, several optimum shortened cyclic codes in the above-mentioned sense have been found. Their code-lengths and generators are tabulated in this paper.     

非系统RS(31,19)编译码算法研究与FPGA实现

针对战术数据链系统低时延数据传输需求,提出一种适用于数据链系统的信道编码方案—非系统缩短码RS(31,19)。本文从MS多项式的观点讨论了非系统RS码的编码和译码算法,并对缩短RS码的编译码算法进行了研究。最后在FPGAEP3SE110上采用了一种改进的BM算法,成功实现RS(31,19)编译码复杂算法,有效提高了译码速度,简化了数据链系统硬件设计。     

Error-correcting codes and B/sub h/-sequences

We construct error-correcting (nonlinear) binary codes using a construction of Bose and Chowla in additive number theory. Our method extends a construction of Graham and Sloane for constant weight codes. The new codes improve 1028 of the 7168 best known h-error-correcting codes of word length /spl les/512 with 1/spl les/h/spl les/14. We give asymptotical comparisons to shortened Bose-Chaudhuri-Hocquenghem (BCH) codes.     

STM-64 linearly repeatered optical transmission experiment usingforward error correcting codes

STM-64 (10 Gbit/s) nonregenerative transmission experiments using forward error correcting codes have been conducted for the first time. Bit errors caused by dispersion in the transmission line and optical noise of Er-doped fibre amplifiers were successfully corrected by using (18880, 18865) and (2370, 2358) shortened Hamming codes     

Comments on “Weighted sum codes for error detection and theircomparison with existing codes”

A.J. McAuley (IEEE/ACM Trans. Networking, vol.2, p.16-22, 1994) proposed a new family of error detection codes called weighted sum codes. In the present paper it is noted, that these codes are equivalent to lengthened Reed Solomon codes, resp. shortened version of lengthened Reed Solomon codes over GF(2^h/2). It is also shown, that it is possible to use these codes for error correction of one error in the code word over GF(2^h/2)     

A class of shortened cyclic codes for a compound channel (Corresp.)

This correspondence presents a class of shortened cyclic codes that are suitable for application on a compound channel. The Chinese remainder theorem is applied to the proof of the error-correcting properties of this class of shortened cyclic codes.     

An error-correcting coding scheme for teletext and othertransparent data broadcasting

Nonprimitive and primitive Reed-Solomon (RS) codes (and product codes based on them) that can provide a very low bit error rate (BER) for the transparent data broadcasting feature of North American broadcast Teletext Specification (NABTS) are described. Transparent data consist of 8-b bytes, each without a parity-check bit, as contrasted with nontransparent data, which consist of 8 bit bytes, each of which has a parity-check bit in every byte. Specific applications for transparent error-coding codes constructed from RS codes in broadcast teletext broadcasting are discussed. Nonprimitive RS codes designed for nontransparent data broadcasting by NABTS teletext are derived, and powerful product forms of shortened nonprimitive Reed-Solomon codes are described     

Design and analysis of codes with distance 4 and 6 minimizing the probability of decoder error

The problem of minimization of the decoder error probability is considered for shortened codes of dimension 2 ^m with distance 4 and 6. We prove that shortened Panchenko codes with distance 4 achieve the minimal probability of decoder error under special form of shortening. This shows that Hamming codes are not the best. In the paper, the rules for shortening Panchenko codes are defined and a combinatorial method to minimize the number of words of weight 4 and 5 is developed. There are obtained exact lower bounds on the probability of decoder error and the full solution of the problem of minimization of the decoder error probability for [39,32,4] and [72,64,4] codes. For shortened BCH codes with distance 6, upper and lower bounds on the number of minimal weight codewords are derived. There are constructed [45,32,6] and [79,64,6] BCH codes with the number of weight 6 codewords close to the lower bound and the decoder error probabilities are calculated for these codes. The results are intended for use in memory devices.     

On binary images of shortened cyclic (8, 5) codes over GF(2/sup 8/)

We have generated binary images of a large number of shortened cyclic (8, 5) codes over GF(2/sup 8/) and have computed weight distributions of the binary images of the codes. Based on the weight distributions, we have chosen four codes with the largest minimum weight 8 and the second largest minimum weight 7 among the generated codes. Over an additive white Gaussian noise channel with binary phase-shift keying modulation, simulation results have shown that block error rates of the chosen codes by a soft-decision decoding based on order-2 reprocessing are smaller than those of (64, 40) subcodes of Reed-Muller (64, 42) code by maximum likelihood decoding.     

On a class of optimal nonbinary linear unequal-error-protectioncodes for two sets of messages

Several authors have addressed the problem of designing good linear unequal error protection (LUEP) codes. However, very little is known about good nonbinary LUEP codes. The authors present a class of optimal nonbinary LUEP codes for two different sets of messages. By combining t-error-correcting Reed-Solomon (RS) codes and shortened nonbinary Hamming codes, they obtain nonbinary LUEP codes that protect one set of messages against any t or fewer symbol errors and the remaining set of messages against any single symbol error. For t⩾2, they show that these codes are optimal in the sense of achieving the Hamming lower bound on the number of redundant symbols of a nonbinary LUEP code with the same parameters