Channel Inclusion Beyond Discrete Memoryless Channels

TL;DR

This paper explores the extension of channel inclusion concepts beyond discrete memoryless channels to additive noise, phase degraded, and MIMO Gaussian channels, analyzing conditions for partial order lattices.

Contribution

It extends the theory of channel inclusion to new channel models and discusses when the partial order forms a lattice.

Findings

Partial order concepts apply to additive noise and phase degraded channels.

Conditions for lattice structures in these channels are identified.

Framework generalizes channel comparison beyond DMCs.

Abstract

Partial ordering of communication channels has applications in performance analysis, and goes beyond comparisons of channels just on the basis of their Shannon capacity or error probability. Shannon defined a partial order of channel inclusion based on convex mixture of input/output degradations of a discrete memoryless channel (DMC). In this paper, extensions to channels other than DMCs are considered. In particular, additive noise channels and phase degraded channels, and multiple input multiple output (MIMO) linear Gaussian channels (LGC) are considered. For each of these models, the conditions under which the partial order becomes a lattice are also discussed.