On the Input-Degradedness and Input-Equivalence Between Channels
Abstract
A channel is said to be input-degraded from another channel if can be simulated from by randomization at the input. We provide a necessary and sufficient condition for a channel to be input-degraded from another one. We show that any decoder that is good for is also good for . We provide two characterizations for input-degradedness, one of which is similar to the Blackwell-Sherman-Stein theorem. We say that two channels are input-equivalent if they are input-degraded from each other. We study the topologies that can be constructed on the space of input-equivalent channels, and we investigate their properties. Moreover, we study the continuity of several channel parameters and operations under these topologies.
Cite
@article{arxiv.1702.00727,
title = {On the Input-Degradedness and Input-Equivalence Between Channels},
author = {Rajai Nasser},
journal= {arXiv preprint arXiv:1702.00727},
year = {2017}
}
Comments
30 pages. Submitted to IEEE Trans. Inform. Theory and in part to ISIT2017. arXiv admin note: substantial text overlap with arXiv:1701.04467