A Characterization of the Shannon Ordering of Communication Channels
Abstract
The ordering of communication channels was first introduced by Shannon. In this paper, we aim to find a characterization of the Shannon ordering. We show that contains if and only if is the skew-composition of with a convex-product channel. This fact is used to derive a characterization of the Shannon ordering that is similar to the Blackwell-Sherman-Stein theorem. Two channels are said to be Shannon-equivalent if each one is contained in the other. We investigate the topologies that can be constructed on the space of Shannon-equivalent channels. We introduce the strong topology and the BRM metric on this space. Finally, we study the continuity of a few channel parameters and operations under the strong topology.
Keywords
Cite
@article{arxiv.1705.01394,
title = {A Characterization of the Shannon Ordering of Communication Channels},
author = {Rajai Nasser},
journal= {arXiv preprint arXiv:1705.01394},
year = {2017}
}
Comments
23 pages, presented in part at ISIT'17. arXiv admin note: text overlap with arXiv:1702.00727