A Distance Between Channels: the average error of mismatched channels
Information Theory
2018-02-07 v1 math.IT
Abstract
Two channels are equivalent if their maximum likelihood (ML) decoders coincide for every code. We show that this equivalence relation partitions the space of channels into a generalized hyperplane arrangement. With this, we define a coding distance between channels in terms of their ML-decoders which is meaningful from the decoding point of view, in the sense that the closer two channels are, the larger is the probability of them sharing the same ML-decoder. We give explicit formulas for these probabilities.
Keywords
Cite
@article{arxiv.1802.02049,
title = {A Distance Between Channels: the average error of mismatched channels},
author = {Rafael G. L. D'Oliveira and Marcelo Firer},
journal= {arXiv preprint arXiv:1802.02049},
year = {2018}
}