Simulation of a Channel with Another Channel

TL;DR

This paper investigates the conditions under which one discrete memoryless channel (DMC) can be simulated from another, providing tight characterizations and introducing new concepts like channel diameter, with implications for understanding channel equivalence.

Contribution

It offers a comprehensive analysis of channel simulation problems, including full characterization for BSC from BEC without shared randomness, and introduces the channel diameter concept.

Findings

Full characterization of BSC from BEC simulation without shared randomness

Infeasibility and achievability results for binary channel simulation

Introduction of the channel diameter with additive and data processing properties

Abstract

In this paper, we study the problem of simulating a DMC channel from another DMC channel under an average-case and an exact model. We present several achievability and infeasibility results, with tight characterizations in special cases. In particular for the exact model, we fully characterize when a BSC channel can be simulated from a BEC channel when there is no shared randomness. We also provide infeasibility and achievability results for simulation of a binary channel from another binary channel in the case of no shared randomness. To do this, we use properties of R\'enyi capacity of a given order. We also introduce a notion of "channel diameter" which is shown to be additive and satisfy a data processing inequality.