Continuity of Channel Parameters and Operations under Various DMC Topologies
Information Theory
2018-05-23 v2 math.IT
Abstract
We study the continuity of many channel parameters and operations under various topologies on the space of equivalent discrete memoryless channels (DMC). We show that mutual information, channel capacity, Bhattacharyya parameter, probability of error of a fixed code, and optimal probability of error for a given code rate and blocklength, are continuous under various DMC topologies. We also show that channel operations such as sums, products, interpolations, and Ar{\i}kan-style transformations are continuous.
Keywords
Cite
@article{arxiv.1701.04466,
title = {Continuity of Channel Parameters and Operations under Various DMC Topologies},
author = {Rajai Nasser},
journal= {arXiv preprint arXiv:1701.04466},
year = {2018}
}
Comments
31 pages. Submitted to IEEE Trans. Inform. Theory and in part to ISIT2017