Parameters of Codes for the Binary Asymmetric Channel

Giuseppe Cotardo; Alberto Ravagnani

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arXiv · 2011.08101

Parameters of Codes for the Binary Asymmetric Channel

Giuseppe Cotardo·Alberto Ravagnani

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Abstract

We introduce two notions of discrepancy between binary vectors, which are not metric functions in general but nonetheless capture the mathematical structure of the binary asymmetric channel. In turn, these lead to two new fundamental parameters of binary error-correcting codes, both of which measure the probability that the maximum likelihood decoder fails. We then derive various bounds for the cardinality and weight distribution of a binary code in terms of these new parameters, giving examples of codes meeting the bounds with equality.

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Giuseppe Cotardo, Alberto Ravagnani. 2020-11-16. Parameters of Codes for the Binary Asymmetric Channel. https://arxiv.org/abs/2011.08101

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