The Error Probability of Generalized Perfect Codes via the Meta-Converse
Information Theory
2018-05-28 v1 math.IT
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.
Cite
@article{arxiv.1805.10025,
title = {The Error Probability of Generalized Perfect Codes via the Meta-Converse},
author = {Gonzalo Vazquez-Vilar and Albert Guillén i Fàbregas and Sergio Verdú},
journal= {arXiv preprint arXiv:1805.10025},
year = {2018}
}
Comments
Submitted to IEEE Transactions on Information Theory