The extended quadratic residue code is the only (48,24,12) self-dual doubly-even code

An extremal self-dual doubly-even binary (n,k,d) code has a minimum weight d=4/spl lfloor/n/24/spl rfloor/+4. Of such codes with length divisible by 24, the Golay code is the only (24,12,8) code, the extended quadratic residue code is the only known (48,24,12) code, and there is no known (72,36,16) code. One may partition the search for a (48,24,12) self-dual doubly-even code into three cases. A previous search assuming one of the cases found only the extended quadratic residue code. We examine the remaining two cases. Separate searches assuming each of the remaining cases found no codes and thus the extended quadratic residue code is the only doubly-even self-dual (48,24,12) code.     

A (48, 31, 8) linear code (Corresp.)

In this paper we construct a linear code having length 48, minimum distance 8, and containing2^{31}codewords. This code is obtained by augmenting a (48,22,8) linear code with2^9- 1 cosets so that the minimum distance is not reduced. The (48,22,8) code used is the direct product of a (16,11,4) extended Hamming code and a (3,2,2) single-parity-check code. The new code has twice as many codewords as the best linear or nonlinear code previously known.     

GPS信号C/A码生成算法设计及仿真实现

全球定位系统(Global Positioning System,GPS)是一种基于卫星的定位系统,向全球范围内的用户全天候提供高精度的导航、定位和授时服务.GPS系统的测距码可以分为粗码(C/A码)和精码(P码),其中C/A码用于民用导航.本文在深入研究C/A码信号生成原理的基础上,利用Matlab对C/A码信号的实现方式进行了仿真实现和分析.仿真结果进一步证实了该方法的正确性和可行性.这对在仿真平台上进一步研究真实环境下的GPS信号,使其能捕获跟踪复杂环境下的卫星信号,改进卫星接收部分的性能有着十分重要的实际意义.     

光通信系统中一种新颖FEC码的仿真分析

基于分组Turbo码（BTC）提出光通信系统中一种新颖前向纠错（FEC）码型,即RS（63,60）×RS（63,60）码。仿真表明,在误码率为10-12时,迭代8次的该BTC与ITU-T G.975.1中迭代3次的RS（255,239）＋CSOC（k0/n0=6/7,J=8）相比,其净编码增益要相应增加0.34dB。分析表明该BTC具有分量码短、编/译码速度快的特点,不仅减小了软/硬件实现的复杂度,而且减小了编/译码带来的时延。因而该新BTC能较好地适用于光通信系统。     

一种新型的融合控制码与数据码的8/10 bit编码器

设计了一种融合控制码(K码)与数据码(D码)、具有无效K码检测功能的高速8/10 bit编码器。深入研究了8/10 bit的编码特点以及K码与D码的内在相关性,提出了将K码融合于D码的改进编码方法。相比传统方法,该编码方法更简单,速度更快,占用逻辑资源更少。采用Verilog HDL语言设计了编码器,使用Modelsim软件对设计进行了功能验证,并利用Quartus II综合实现了8/10 bit编码电路。该编码器可直接应用于需要8/10 bit编码的收发器。     

Applications of low-density parity-check codes to magneticrecording channels

We consider the use of high-rate low-density parity-check (LDPC) codes for magnetic recording. We design and evaluate the performance of a magnetic recording system, which uses an LDPC code as the error-correcting code, in conjunction with a rate 16/17 quasimaximum-transition-run (QMTR) channel code on a modified E² PR4 (ME²PR4)-equalized channel. Iterative decoding between the partial response channel and the LDPC code is performed. Simulations show that an additional four-dB gain over the QMTR code can be obtained by the LDPC code. The algorithms used to design this LDPC code are also discussed     

Code placement and replacement schemes for WCDMA Rotated-OVSF code tree management

Orthogonal variable spreading factor (OVSF) channelization codes are widely used to provide variable data rates for supporting different bandwidth requirements in wideband code division multiple access (WCDMA) systems. Many novel works in the literature have intensively investigated code placement and replacement schemes in OVSF code trees to reduce the code blocking probability and the code reassignment cost. In this paper, we introduce a new code tree structure, namely, a rotated-orthogonal variable spreading factor (ROVSF) code tree, whose code capacity is the same as that of the traditional OVSF code tree. This work addresses both code placement and replacement schemes in the ROVSF code tree system, where ROVSF codes can be used at the forward link of WCDMA systems. Some valuable properties of the developed ROVSF code tree are presented to develop code placement/replacement schemes with lower code blocking probability and less code reassignment cost. The main contribution of our scheme is to identify linear-code chains (LCCs) and nonlinear-code trees (NCTs) in the ROVSF code tree. This work exploits the unsequence property of linear-code chains to design a new code placement and replacement mechanism. Our code placement/ replacement schemes initially attempt to allocate request codes on LCCs and, then, to allocate them to NCTs. Using LCCs with the unsequence property allows us to efficiently reduce the code blocking probability and the code reassignment cost. Extensive simulations are conducted to illustrate that our code placement/replacement results based on the ROVSF code tree actually improve the code blocking probability and the code reassignment cost.     

A Novel ZCZ Code Based on m-Sequences and its Applications in CDMA Systems

In this paper, we propose a novel zero-correlation zone (ZCZ) code, called m-ZCZ code. Both auto-correlation function (ACF) side lobes and cross-correlation function (CCF) of the code are zero within ZCZ, whose length can be adjusted in a very.'flexible manner. The m-ZCZ code can be generated using a simple method. If compared with conventional binary ZCZ codes, the m-ZCZ code can support more users while still retaining the same interference-resist capability.     

Smoothed DPCM codes

Interpolative differential pulse code modulation (IDPCM) is known to outperform DPCM at rate 1 b/sample for several synthetic source models. The authors use minimum-mean-squared error (MMSE) fixed-lag smoothing with DPCM to develop a code generator using delayed decoding. This smoothed DPCM (SDPCM) code generator is compared to DPCM and IDPCM code generators at rates 1 and 2 b/sample for tree coding several synthetic sources and to a DPCM code generator at 2 b/sample for speech sources     

On MDS extensions of generalized Reed- Solomon codes

An(n, k, d)linear code overF=GF(q)is said to be {em maximum distance separable} (MDS) ifd = n - k + 1. It is shown that an(n, k, n - k + 1)generalized Reed-Solomon code such that2leq k leq n - lfloor (q - 1)/2 rfloor (k neq 3 {rm if} qis even) can be extended by one digit while preserving the MDS property if and only if the resulting extended code is also a generalized Reed-Solomon code. It follows that a generalized Reed-Solomon code withkin the above range can be {em uniquely} extended to a maximal MDS code of lengthq + 1, and that generalized Reed-Solomon codes of lengthq + 1and dimension2leq k leq lfloor q/2 rfloor + 2 (k neq 3 {rm if} qis even) do not have MDS extensions. Hence, in cases where the(q + 1, k)MDS code is essentially unique,(n, k)MDS codes withn > q + 1do not exist.     

Study on New Concatenated Code in WDM Optical Transmission Systems

A new concatenated code of RS（255,239）＋BCH（2 040,1 930） code to he suitable for WDM optical transmission systems is proposed. The simulation resuhs show that this new concatenated code. compared with the RS（255,239）4-CSOC（k0/n0=6/7, J= 8） code in ITU-TG. 75.1, has a lower redundancy and better error-correction performance, furthermore, its net coding gain（NCG） is respectively 0. 46 dB, 0.43 dB morethanthatofRS（255,239）＋CSOC（k0/n0= 6/7, J= 8） code and BCH（3860,3824）＋BCH （2 040,1 930） code in ITU TG. 75. 1 at the third iteration for the bit error rate（BER） of 10^-12. Therefore, the new super forward error correction（Super-FEC） concatenated code can be better used in ultra long-haul, ultra large-capacity and ultra high-speed WDM optical communication systems.     

基于循环中国剩余定理和改进的PEG算法的IRA码

为了避免交织器产生的时延,通过改进的渐进边增长(PEG)算法和循环中国剩余定理构造了一种不规则重复累积(IRA)码.与常规的IRA码相比,提出的码字具有半随机半结构化形式,不需要设计交织器,且码长选择更加灵活.仿真结果显示,在码率为1/2的条件下,当误码率为10-6时,构造的IRA(1 000,500)码与PEG-IRA(1 000,500)码和基于剩余类数对的IRA(1 000,500)码相比,在对应的相同条件下分别取得了0.2 dB和0.1 dB左右的净编码增益提升;且在码率为3/4时,所构造的IRA(16 200,11 880)码比相同码长和码率的DVB-S2标准LDPC码净编码增益提高了约0.1 dB左右.     

Limit distribution of the minimum distance of random linear codes

The distribution of the ratio of minimum distance to code length of a random linear code approaches a step distribution as the code length becomes arbitrarily large at fixed code rate. The location of the step is at the smaller value ofpsatisfying1 + p log_{2}p + (1 - p) log_{2} (1 - p) = k/n.     

MIMO GS OVSF/OFDM Based Underwater Acoustic Multimedia Communication Scheme

An underwater acoustic multimedia communication (UWAMC) system is proposed with 2400 transmission modes according to time-varying multipath underwater acoustic (UWA) channel conditions. The orthogonal variable spreading factor (OVSF) scheme and Gold sequence (GS) scramble code are integrated into multi-input multi-output UWAMC system based on orthogonal frequency-division multiplexing to achieve the quality of service of multimedia transmission in the UWA channel. Binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK) adaptive modulation, direct mapping (DM) or space–time block code (STBC) transmission strategies, convolution channel code with rate 1/2 and 1/3, and a power assignment mechanism were adopted in the proposed system. Simulation results show that the bit error rate (BER) and power saving ratio (PSR) performance of the STBC strategy with transmission diversity is superior to that of the DM strategy without transmission diversity, and the performance of the BERs and PSRs of the transmission scheme with the GS scramble code surpasses that of the scheme without the code. The performance of the BERs and PSRs of BPSK modulation with a channel code rate of 1/3 is better than that of BPSK modulation with a channel code rate of 1/2, and the performances of BERs and PSRs of BPSK modulation with a channel code rate of 1/3 are better than that of QPSK modulation with a channel code rate of 1/3. As the length of the OVSF codes increases, the UWAMC system’s BERs decrease, and its PSRs increase. The UWAMC system can achieve either maximum transmission speed or maximum transmission power efficiency.     

On algebraic decoding of the Z4-linearCalderbank-McGuire code

The quaternary Calderbank-McGuire (see Des., Codes Cryptogr., vol.10, no.2, 1997) code is a Z₄-linear code of length 32 which has 2³⁷ codewords and a minimum Lee distance of 12. The Gray map of this code is known to be a nonlinear binary (64, 2³⁷,12) code. The Z₄-linear Calderbank-McGuire code can correct all errors with Lee weight ⩽5. An algebraic decoding algorithm for the code is presented in this paper. Furthermore, we discuss an alternative decoding method which takes advantage of the efficient BCH decoding algorithm     

Bounds for abnormal binary codes with covering radius one

The normality of binary codes is studied. The minimum cardinality of a binary code of length n with covering radius R is denoted by K(n,R). It is assumed that C is an (n,M)R code, that is, a binary code of length n with M codewords and covering radius R. It is shown that if C is an (n,M)1 code, then it is easy to find a normal (n ,M)1 code by changing C in a suitable way, and that all the optimal (n,M)1 codes (i.e. those for which M=K(n,1)) are normal and their every coordinate is acceptable. It is shown that if C is an abnormal (n,M) code, then n⩾9, and an abnormal (9118)1 code which is the smallest abnormal code known at present, is constructed. Lower bounds on the minimum cardinality of a binary abnormal code of length n with covering radius 1 are derived, and it is shown that if an (n,M)1 code is abnormal, then M⩾96     

Universal Models for the Exponential Distribution

This paper considers the problem of constructing information theoretic universal models for data distributed according to the exponential distribution. The universal models examined include the sequential normalized maximum likelihood (SNML) code, conditional normalized maximum likelihood (CNML) code, the minimum message length (MML) code, and the Bayes mixture code (BMC). The CNML code yields a codelength identical to the Bayesian mixture code, and within O(1) of the MML codelength, with suitable data driven priors.     

On the Hardness of Decoding the Gale–Berlekamp Code

The Gale–Berlekamp (in short, GB) code is the dual code of the binary product code in which the horizontal and vertical constituent codes are both the parity code. It is shown that the problem of deciding whether there is a codeword of the GB code within a prescribed distance from a given received word, is NP-complete. The problem remains hard (in a well-defined sense) even if the decoder is allowed unlimited preprocessing that depends only on the code length. While the intractability of maximum-likelihood decoding (MLD) for specific codes has already been shown by Bruck and Naor, Lobstein, and Guruswami and Vardy, the result herein seems to be the first that shows hardness for a “natural” code (in particular, without any tailoring of the definition or the parameters of the code to suit the hardness proof). In contrast, it is also shown that, with respect to any memoryless binary-symmetric channel (BSC) with crossover probability less than $1/2$ , MLD can be implemented in linear time for all error events except for a portion that occurs with vanishing probability.      

Context-dependent multilevel pattern matching for lossless image compression

In this paper, the multilevel pattern matching (MPM) code for compression of one-dimensional (1D) sequences is first generalized to compress two-dimensional (2D) images, resulting in a 2D multilevel pattern matching (MPM) code. It is shown that among all images of n pixels, the worst case redundancy of the 2D MPM code against any finite-template-based arithmetic code is O(1//spl radic/logn). This result contrasts unfavorably with the fact that among all 1D sequences of length n, the MPM code has a worst case redundancy of O(1/logn) against any finite-state arithmetic code; this is caused by the so-called 2D boundary effect. To alleviate the 2D boundary effect, we extend the 2D MPM code to the case of context modeling, yielding a context-dependent 2D MPM code. It is shown that among all images of n pixels, the context-dependent 2D MPM code has an O(1/logn) worst case redundancy against any finite-template-based arithmetic code satisfying a mild condition; this redundancy is better than that of the 2D MPM code without context models. Experimental results demonstrate that the context-dependent 2D MPM code significantly outperforms the 2D MPM code without context models for bi-level images. It is also demonstrated that, in terms of compression rates, the context-dependent 2D MPM code performs significantly better than the progressive coding mode of JBIG1 for both textual and bi-level images, and better than or comparably to the sequential coding mode of JBIG1 and JBIG2. In addition to its excellent compression performance, the context-dependent 2D MPM code allows progressive transmission of images.     

Weight distributions of some classes of binary cyclic codes (Corresp.)

Leth_1(x)h_2(x)be the parity-check polynomial of a binary cyclic code. This correspondence presents a formula for decomposing words in the code as sums of multiples of words in the codes whose parity-check polynomials areh_1(x)andh_2(x). This decomposition provides information about the weight distribution of the code.