aqora

Channel Metrization

Rafael G. L. D’Oliveira, Marcelo Firer

We present an algorithm that, given a channel, determines if there is a distance for it such that the maximum likelihood decoder coincides with the minimum distance decoder. We also show that any metric, up to a decoding equivalence, can be isometrically embedded into the hypercube with the Hamming metric, and thus, in terms of decoding, the Hamming metric is universal.

arXiv:1510.03104Oct 11, 20155 citations

Maximum Likelihood Decoding of Codes on the Z-channel

Ángela I. Barbero, Pål Gunnar Ellingsen, Susanna Spinsante +1 more

The aim of this paper is to extend some basic concepts related to the Maximum Likelihood decoding of codes on the Z-channel, which is a particular, but very important, example of an asymmetric channel. We study distance properties of linear codes over the Z-channel, in order to define a suitable metric for the implementation of a Maximum Likelihood decoder on the channel. A combinatorial expression for an approximation on the probability of incorrect Maximum Likelihood decoding is also provided, and comparisons are given to evaluate the tightness of the estimation, when a Hamming code, a Turbo code and an LDPC code are used for communicating over the Z-channel.The aim of this paper is to extend some basic concepts related to the Maximum Likelihood decoding of codes on the Z-channel, which is a particular, but very important, example of an asymmetric channel. We study distance properties of linear codes over the Z-channel, in order to define a suitable metric for the implementation of a Maximum Likelihood decoder on the channel. A combinatorial expression for an approximation on the probability of incorrect Maximum Likelihood decoding is also provided, and comparisons are given to evaluate the tightness of the estimation, when a Hamming code, a Turbo code and an LDPC code are used for communicating over the Z-channel.

International Conference on CommunicationsJan 1, 20065 citations

On the Optimality of the Hamming Metric for Decoding Block Codes over Binary Additive Noise Channels

Ghady Azar

Most of the basic concepts of algebraic coding theory are derived for the memoryless binary symmetric channel. These concepts do not necessarily hold for time-varying channels or for channels with memory. However, errors in real-life channels seem to occur in bursts rather than independently, suggesting that these channels exhibit some statistical dependence or memory. Nonetheless, the same algebraic codes are still commonly used in current communication systems that employ interleaving to spread channel error bursts over the set of received codewords to make the channel appear memoryless to the block decoder. This method suffers from immediate shortcomings as it fails to exploit the channel’s memory while adding delay to the system. We study optimal maximum likelihood block decoding of binary codes sent over several binary additive channels with infinite and finite memory. We derive conditions on general binary codes and channels parameters under which maximum likelihood and minimum distance decoding are equivalent. The channels considered in this work are the infinite and finite memory Polya contagion channels [1],Most of the basic concepts of algebraic coding theory are derived for the memoryless binary symmetric channel. These concepts do not necessarily hold for time-varying channels or for channels with memory. However, errors in real-life channels seem to occur in bursts rather than independently, suggesting that these channels exhibit some statistical dependence or memory. Nonetheless, the same algebraic codes are still commonly used in current communication systems that employ interleaving to spread channel error bursts over the set of received codewords to make the channel appear memoryless to the block decoder. This method suffers from immediate shortcomings as it fails to exploit the channel’s memory while adding delay to the system. We study optimal maximum likelihood block decoding of binary codes sent over several binary additive channels with infinite and finite memory. We derive conditions on general binary codes and channels parameters under which maximum likelihood and minimum distance decoding are equivalent. The channels considered in this work are the infinite and finite memory Polya contagion channels [1],

Jan 1, 20131 citation

On maximum likelihood soft decision decoding of binary Hamming codes

P.A.H. Bours, N.J.C. Lous, Henk C. A. van Tilborg

Jan 1, 19910 citations

On maximum likelihood soft decision syndrome decoding

M.P.C. Fossorier, Shu Hwa Lin, J. Synders

Maximum likelihood decoding of binary linear block codes is addressed by combining the approaches of processing the generator matrix G and parity-check matrix H.

IEEE International Symposium on Information Theory (ISIT)Nov 19, 20022 citations

Ellipsoidal coverings and error-free search in maximum likelihood decoding

Ilya I. Dumer

For general linear (n, k) codes, maximum likelihood decoding is performed by random search of error-free k-subsets. The lowest known complexity of soft-decision decoding is obtained.

IEEE International Symposium on Information Theory (ISIT)Nov 27, 20020 citations

Matched Metrics and Channels

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Matched Metrics and Channels

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