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arXiv · 1805.10025

The Error Probability of Generalized Perfect Codes via the Meta-Converse

Gonzalo Vazquez-Vilar·Albert Guillén i Fàbregas·Sergio Verdú
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Abstract

We introduce a definition of perfect and quasi-perfect codes for symmetric channels parametrized by an auxiliary output distribution. This notion generalizes previous definitions of perfect and quasi-perfect codes and encompasses maximum distance separable codes. The error probability of these codes, whenever they exist, is shown to coincide with the estimate provided by the meta-converse lower bound. We illustrate how the proposed definition naturally extends to cover almost-lossless source-channel coding and lossy compression.

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Gonzalo Vazquez-Vilar, Albert Guillén i Fàbregas, Sergio Verdú. 2018-05-25. The Error Probability of Generalized Perfect Codes via the Meta-Converse. https://arxiv.org/abs/1805.10025

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