English

On the Input-Degradedness and Input-Equivalence Between Channels

Information Theory 2017-02-03 v1 math.IT

Abstract

A channel WW is said to be input-degraded from another channel WW' if WW can be simulated from WW' 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 WW' is also good for WW. 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

R2 v1 2026-06-22T18:07:50.926Z