Topic
Sequential decoding
About: Sequential decoding is a research topic. Over the lifetime, 8667 publications have been published within this topic receiving 204271 citations.
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09 Jul 2006
TL;DR: An efficient algorithm that solves the minimal polynomial of the ideal of interpolating polynomials with respect to a certain monomial order is presented based on the theory of Grobner bases of modules.
Abstract: A central problem of algebraic soft-decision decoding of Reed-Solomon codes is to find the minimal polynomial of the ideal of interpolating polynomials with respect to a certain monomial order. An efficient algorithm that solves the problem is presented based on the theory of Grobner bases of modules.
57 citations
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27 Jun 2004TL;DR: Convolutional network codes are considered for cyclic graphs and coefficients of lower polynomial degree are drawn to consideration in order to minimize the memory and overhead.
Abstract: Convolutional network codes are considered for cyclic graphs. In CNC each node receives several streams and generates output streams whose current symbols depend on the current input symbols and previous input symbols in the node memory. A multicast CNC can be constructed using an algorithm, in order to minimize the memory and overhead, coefficients of lower polynomial degree are drawn to consideration. For CNC the overhead is the initial delay before the sinks start receiving symbols. CNC with the sequential decoder achieves good performance for some networks.
56 citations
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TL;DR: A novel density evolution approach to analyze the iterative decoding algorithms of low-density parity-check (LDPC) codes and product codes, based on Gaussian densities, is proposed, whose iterates directly represent the error probability both for the additive white Gaussian noise (AWGN) and the Rayleigh-fading channel.
Abstract: We propose a novel density evolution approach to analyze the iterative decoding algorithms of low-density parity-check (LDPC) codes and product codes, based on Gaussian densities. Namely, for these classes of codes we derive a one-dimensional (1D) map whose iterates directly represent the error probability both for the additive white Gaussian noise (AWGN) and the Rayleigh-fading channel. These simple models allow a qualitative analysis of the nonlinear dynamics of the decoding algorithm. As an application, we compute the decoding thresholds and show that they are consistent with the simulation results available in the literature.
56 citations
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TL;DR: Two modifications of the basic correlation decoding approach are presented, one of them yields a nonexhaustive optimum word decoding algorithm whose complexity depends upon the "projecting" structure of the code.
Abstract: Two modifications of the basic correlation decoding approach are presented. One of them yields a nonexhaustive optimum word decoding algorithm whose complexity depends upon the "projecting" structure of the code. This algorithm is then modified to yield a second decoding algorithm which, while not optimum, has simpler complexity. Applications to the AWGN channel are discussed and performance curves are given for (24, 12) and (31, 15) codes.
56 citations
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TL;DR: It is shown that the proposed suboptimum, algorithm has better performance compared with generalized minimum distance decoding, while the proposedMLD algorithm has significantly lower decoding complexity than the well-known Vardy-Be'ery (1991) MLD algorithm.
Abstract: This paper presents a maximum-likelihood decoding (MLD) and a suboptimum decoding algorithm for Reed-Solomon (RS) codes. The proposed algorithms are based on the algebraic structure of the binary images of RS codes. Theoretical bounds on the performance are derived and shown to be consistent with simulation results. The proposed suboptimum algorithm achieves near-MLD performance with significantly lower decoding complexity. It is also shown that the proposed suboptimum, algorithm has better performance compared with generalized minimum distance decoding, while the proposed MLD algorithm has significantly lower decoding complexity than the well-known Vardy-Be'ery (1991) MLD algorithm.
56 citations