We consider the set M = {(a, b): a = bh mod x(2t)} of all solutions of the key equation for alternant codes, where h is the syndrome polynomial. In decoding these codes a particular solution (omega, sigma) is an eleme...
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We consider the set M = {(a, b): a = bh mod x(2t)} of all solutions of the key equation for alternant codes, where h is the syndrome polynomial. In decoding these codes a particular solution (omega, sigma) is an element of M is sought, subject to omega and sigma being relatively prime and satisfying certain degree conditions. We prove that these requirements specify (omega, sigma) uniquely as the minimal element of M (analogous to the monic polynomial of minimal degree generating an ideal of F[x]) with respect to a certain term order and that, as such, (w, a) may be determined from an appropriate Grobner basis of M. Motivated by this and other variations of the key equation (such as that appropriate to errors-and-erasures decoding) we derive a general algorithm for solving the congruence a = bg mod x(n) for a range of term orders defined by the conditions on the particular solution required. Our techniques provide a unified approach to the solution of these key equations.
The word error probability of linear block codes is computed for diversity systems with maximal ratio combining in mobile communications with three decoding algorithms: error correction (EC), error/erasure correction ...
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The word error probability of linear block codes is computed for diversity systems with maximal ratio combining in mobile communications with three decoding algorithms: error correction (EC), error/erasure correction (EEC), and maximum likelihood (ML) soft decoding algorithm. Ideal interleaving is assumed. EEC gives 0.1-1.5 dB gain over EC. The gain of EEC over EC decreases as the number of diversity channels increases. ML soft gives 1.8-5.5 dB gain over EC.
The article reports on the characteristics of an algorithm that implements generalized minimum distance (GMD) decoding of Reed-Solomon codes. The algorithm uses the novel Welch-Berlekamp (WB) algorithm, as modified by...
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The article reports on the characteristics of an algorithm that implements generalized minimum distance (GMD) decoding of Reed-Solomon codes. The algorithm uses the novel Welch-Berlekamp (WB) algorithm, as modified by Tze-Hua, in order to minimize the complexity of the decoder. Both the WB algorithm and the GMD extension of the WB algorithm are described in outline. The performance of the GMD algorithm was simulated on AWGN channels and fading channels. Results are presented both for RS and concatenated RS codes. The gains over conventional decoding are larger for fading channels than for AWGN conditions but seem useful in all cases. The complexities of the GMD algorithm and the WB algorithm are analysed and compared to that of conventional RS decoding algorithms.
Disjoint uniquely decodable codebooks for noiseless synChronized multiple-access adder channels are studied. Codebooks are applicable to multiple-access systems in which the number of transmitting users varies over th...
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Disjoint uniquely decodable codebooks for noiseless synChronized multiple-access adder channels are studied. Codebooks are applicable to multiple-access systems in which the number of transmitting users varies over the life of the system. Several designs of codebooks, based on certain integer sets from {0, 1, 2, 3, ..., 2n - 1), are presented. They are restricted to codebooks which have the rate sum above one and simple and efficient decoding algorithms.
Classes of systematic codes correcting burst asymmetric or unidirectional errors are proposed. These codes have less check bits than ordinary burst error correcting codes. decoding algorithms for the proposed codes ar...
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Classes of systematic codes correcting burst asymmetric or unidirectional errors are proposed. These codes have less check bits than ordinary burst error correcting codes. decoding algorithms for the proposed codes are also presented. Encoding and decoding of the codes is very easy.
The letter describes a comparison of some receiver structures suitable for trellis-coded modulation on channels causing intersymbol interference. Simulation results show that a Viterbi decoder treating trellis coding ...
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The letter describes a comparison of some receiver structures suitable for trellis-coded modulation on channels causing intersymbol interference. Simulation results show that a Viterbi decoder treating trellis coding and intersymbol interference as one compound encoding mechanism yields the best performance, which at Pb=10-4 is about 6 dB in S/N better than any other receiver structure
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