Source and Channel Simulation Using Arbitrary Randomness

TL;DR

This paper establishes necessary and sufficient conditions for approximating channels by sources and for source simulation, using variational distance, without complex optimization, and illustrates results with non-ergodic examples.

Contribution

It provides new, easily testable conditions for source and channel approximation that do not require solving optimization problems.

Findings

Conditions based on individual source and channel properties

Approximation criteria use vanishing variational distance

Applicable to non-ergodic examples

Abstract

Necessary and sufficient conditions for approximation of a general channel by a general source are proved. For the special case in which the channel input is deterministic, which corresponds to source simulation, we prove a stronger necessary condition. As the approximation criteria, vanishing variational distance between the original and the approximated quantity is used for both of the problems. Both necessary and sufficient conditions for the two problems are based on some individual properties of the sources and the channel and are relatively easy to evaluate. In particular, unlike prior results for this problem, our results do not require solving an optimization problem to test simulatability. The results are illustrated with several non-ergodic examples.