卡氏积码的MDR码和自对偶码

定义了Z_(r_1),Z_(r_2)…,Z_(r_s)上线性码C_1,C_2,…,C_s的卡氏积码.利用子模同构定理,研究了在Z_(r_1)×Z_(r_2)×…×Z_(r_s)上卡氏积码C_1×C_2×…×C_s的秩与在Z_(r_1),Z_(r_2),…,Z_(r_s)码C_1,C_2,…,C_s的秩的关系,借助这一关系,得到了MDR码的卡氏积仍为MDR码和自对偶码的卡氏积码也为自对偶码.     

Quantum codes from concatenated algebraic-geometric codes

We apply Steane's enlargement of the Calderbank-Shor-Steane (CSS) codes and additive codes over F/sub 4/ to concatenated algebraic-geometric codes to construct many good quantum codes with fewer restrictions on the parameters compared to some known quantum codes. Some of the quantum codes we have constructed are either optimal or have parameters as good as the best known codes, while some have parameters better than those obtained from other known constructions.     

Zigzag codes and concatenated zigzag codes

This paper introduces a family of error-correcting codes called zigzag codes. A zigzag code is described by a highly structured zigzag graph. Due to the structural properties of the graph, very low-complexity soft-in/soft-out decoding rules can be implemented. We present a decoding rule, based on the Max-Log-APP (MLA) formulation, which requires a total of only 20 addition-equivalent operations per information bit, per iteration. Simulation of a rate-1/2 concatenated zigzag code with four constituent encoders with interleaver length 65 536, yields a bit error rate (BER) of 10^-5 at 0.9 dB and 1.3 dB away from the Shannon limit by optimal (APP) and low-cost suboptimal (MLA) decoders, respectively. A union bound analysis of the bit error probability of the zigzag code is presented. It is shown that the union bounds for these codes can be generated very efficiently. It is also illustrated that, for a fixed interleaver size, the concatenated code has increased code potential as the number of constituent encoders increases. Finally, the analysis shows that zigzag codes with four or more constituent encoders have lower error floors than comparable turbo codes with two constituent encoders     

Weighted Reed-Muller codes and algebraic-geometric codes

A generalization of the Reed-Muller codes, the weighted Reed-Muller codes, is presented. The code parameters are estimated and the duals are shown also to be weighted Reed-Muller codes. It is shown how the minimum distance of certain algebraic-geometric codes in many cases can be determined exactly or an upper bound can be found, using subcodes which are weighted Reed-Muller codes     

Linear codes derived from cyclic codes

This paper presents a procedure for the construction of linear block codes derived from cyclic subspaces. The distance properties of these codes are determined indirectly by the BCH bound despite the fact that they are not cyclic.     

之型码和级联之型码

本文介绍了一种新型的纠错码，称之为“之型码”。之型码可以形成非常简捷的软输入/软输出译码规则，我们在Max-Log-MAP(MLM)译码方法的基础上提出了一种译码规则，这一译码规则的计算复杂度为每次迭代计算单位信息比特大约需要20次加法运算操作。在仿真实验中，我们用最优译码器和更简捷的次最优译码器进行译码时，其性能在误比特率为10^-5处分别距香农理论极限仅0.9dB和1.4dBH。此外，上述码字与2维turbo码相比具有更低的误码基底值（error floor）。     

Joint source-channel decoding of variable-length codes for convolutional codes and turbo codes

Several recent publications have shown that joint source-channel decoding could be a powerful technique to take advantage of residual source redundancy for fixed- and variable-length source codes. This letter gives an in-depth analysis of a low-complexity method recently proposed by Guivarch et al., where the redundancy left by a Huffman encoder is used at a bit level in the channel decoder to improve its performance. Several simulation results are presented, showing for two first-order Markov sources of different sizes that using a priori knowledge of the source statistics yields a significant improvement, either with a Viterbi channel decoder or with a turbo decoder.     

Joint source-channel codes based on irregular turbo codes and variable length codes

Variable length codes (VLCs), used in data compression, are very sensitive to error propagation in the presence of noisy channels. To address this problem, several joint sourcechannel turbo techniques have been proposed in the literature. In this paper, we focus on pairs of source/VLC of low redundancy, i.e., when there is a good match between the source statistics and the length distribution of the VLC. It is a case not considered extensively in the literature so far and the classical concatenation of a VLC and a convolutional code is not satisfying. Through EXIT chart and interleaving gain analysis, we show that the introduction of a repetition code between the VLC and the convolutional code considerably improves global performance. In particular, excellent symbol error rates are obtained with reversible VLCs which are used in recent source codecs.     

从素数码到级联素数码

研究级联素数码与素数码的关系，得出级联素数码是由素数码序列时移、频移后级联得到的构造思想，并得出具体时移规律和频移规律。这一结论对于研究素数码在其他有限扩域GF（W），n〉2上的扩展具有启发意义。此外，根据素数码时移与频移等价的性质，得出得到具有理想汉明相关特性的跳频序列组的分组规律，即同一分组中，所有序列对应的时移步长对相同，为选择具有理想汉明相关特性的跳频序列组提供了理论依据。最后列出基于上述结论的仿真模型。     

DC-free error-correcting codes based on convolutional codes

A new construction of direct current (DC)-free error-correcting codes based on convolutional codes is proposed. The new code is constructed by selecting a proper subcode from a convolutional code composed of two different component codes. The encoder employs a Viterbi algorithm as the codeword selector so that the selected code sequences satisfy the DC constraint. A lower bound on the free distance of such codes is proposed, and a procedure for obtaining this bound is presented. A sufficient condition for these codes to have a bounded running digital sum (RDS) is proposed. Under the assumption of a simplified codeword selection algorithm, we present an upper bound on the maximum absolute value of the RDS and derive the sum variance for a given code. A new construction of standard DC-free codes, i.e., DC-free codes without error-correcting capability, is also proposed. These codes have the property that the decoder can be implemented by simple symbol-by-symbol hard decisions. Finally, under the new construction, we propose several codes that are suitable for the systems that require small sum variance and good error-correction capability     

Universal space-time codes from demultiplexed trellis codes

In broadcast scenarios or in the absence of accurate channel probability distribution information, code design for consistent channel-by-channel performance, rather than average performance over a channel distribution, may be desirable. Root and Varaiya's compound channel theorem for linear Gaussian channels promises the existence of universal codes that operate reliably whenever the channel mutual information (MI) is above the transmitted rate. This paper presents two-dimensional trellis codes that provide such universal performance over the compound linear vector Gaussian channel when demultiplexed over two, three, and four transmit antennas. The presented trellis codes, found by exhaustive search, guarantee consistent performance on every matrix channel that supports the information transmission rate with an MI gap that is similar to the capacity gap of a well-designed additive white Gaussian noise (AWGN)-specific code on the AWGN channel. As a result of their channel-by-channel consistency, the universal trellis codes presented here also deliver comparable, or, in some cases, superior, frame-error rate and bit-error rate performance under quasi-static Rayleigh fading, as compared with trellis codes of similar complexity that are designed specifically for the quasi-static Rayleigh-fading scenario.     

Beyond stabilizer codes II: Clifford codes

For pt. I see ibid., vol.48, no.8, p.2392-95 (2002). Knill (1996) introduced a generalization of stabilizer codes, called Clifford codes. It remained unclear whether or not Clifford codes can be superior to stabilizer codes. We show that Clifford codes are stabilizer codes provided that the abstract error group has an Abelian index group. In particular, if the errors are modeled by tensor products of Pauli matrices, then the associated Clifford codes are necessarily stabilizer codes.     

Self-synchronizing codes derived from binary cyclic codes

The sensitivity of a binary block code to loss of synchronism (misplacement of the "commas" separating codewords) can be characterized by a pair of numbers[s, delta]such that any synchronization slip of s bits or less produces an overlap sequence differing from a legitimate codeword in at leastdeltaplaces. This definition is broader than that of comma freedom of indexdelta, which is included as the special case of s equal to the integer part of half the code block length. For codes having the slip-detecting characteristic[s, delta]there exists the possibility of implementation to restore synchronism during an interval relatively free from bit errors. It is shown that certain error-correcting binary cyclic block codes can be altered to obtain the characteristic[s, delta]by the addition of a fixed binary vector to each codeword prior to transmission. These altered cyclic codes retain the full error-correcting power of the original cyclic codes. An error-detecting/correcting data format providing protection against the acceptance of misframed data is thus obtained without the insertion of special synchronizing sequences into the bit stream.     

Sphere-bound-achieving coset codes and multilevel coset codes

A simple sphere bound gives the best possible tradeoff between the volume per point of an infinite array L and its error probability on an additive white Gaussian noise (AWGN) channel. It is shown that the sphere bound can be approached by a large class of coset codes or multilevel coset codes with multistage decoding, including certain binary lattices. These codes have structure of the kind that has been found to be useful in practice. Capacity curves and design guidance for practical codes are given. Exponential error bounds for coset codes are developed, generalizing Poltyrev's (1994) bounds for lattices. These results are based on the channel coding theorems of information theory, rather than the Minkowski-Hlawka theorem of lattice theory     

Coset codes viewed as terminated convolutional codes

Coset codes are considered as terminated convolutional codes. Based on this approach, three new general results are presented. First, it is shown that the iterative squaring construction can equivalently be defined from a convolutional code whose trellis terminates. This convolutional code determines a simple encoder for the coset code considered, and the state and branch labelings of the associated trellis diagram become straightforward. Also, from the generator matrix of the code in its convolutional code form, much information about the trade-off between the state connectivity and complexity at each section, and the parallel structure of the trellis, is directly available. Based on this generator matrix, it is shown that the parallel branches in the trellis diagram of the convolutional code represent the same coset code C₁ of smaller dimension and shorter length. Utilizing this fact, a two-stage optimum trellis decoding method is devised. The first stage decodes C₁ while the second stage decodes the associated convolutional code, using the branch metrics delivered by stage 1. Finally, a bidirectional decoding of each received block starting at both ends is presented. If about the same number of computations is required, this approach remains very attractive from a practical point of view as it roughly doubles the decoding speed. This fact is particularly interesting whenever the second half of the trellis is the mirror image of the first half, since the same decoder can be implemented for both parts     

Good block codes derived from cyclic codes

By combining irreducible cyclic codes, we obtain good quasicyclic or extended quasicyclic codes. Some of these improve on the lower bound of Helgert and Stinaff.     

Superimposed codes based on punctured convolutional codes

Punctured convolutional codes of rates k₁/n and k₂ /n are applied to |u|u+v construction, and then a superimposed code of rate (k₁+k₂)/(2n) is constructed. A suboptimal decoding procedure is presented for the superimposed codes, and it reduces the decoding complexity as compared with maximum likelihood decoding for the known convolutional codes     

线性等距码与极大投射码

本文证明任意有限域上的一个线性等距码等价于一个极大投射码的重复码,从而给出了一般q元线性等距码的全部结构。     

P2 codes: pragmatic trellis codes utilizing puncturedconvolutional codes

A single convolutional code of fixed rate can be punctured to form a class of higher rate convolutional codes. The authors extend this pragmatic approach to the case where the core of the trellis decoder is a Viterbi decoder for a punctured version of the de facto standard, rate 1/2 convolutional code