On the Input-Degradedness and Input-Equivalence Between Channels

Abstract

A channel $W$ is said to be input-degraded from another channel $W^{\prime }$ if $W$ can be simulated from $W^{\prime }$ 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 $W^{\prime }$ is also good for $W$. 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.

arXiv comment30 pages. Submitted to IEEE Trans. Inform. Theory and in part to ISIT2017. arXiv admin note: substantial text overlap with arXiv:1701.04467