Sequential Channel Synthesis

TL;DR

This paper studies the sequential channel synthesis problem, providing a complete characterization of optimal solutions in point-to-point, broadcast, and interactive scenarios, highlighting when symbol-by-symbol mappings are optimal.

Contribution

It offers the first complete single-letter characterization for the sequential channel synthesis problem across multiple communication scenarios.

Findings

Symbol-by-symbol mapping is not always optimal.

Complete solutions are provided for point-to-point and interactive cases.

Bounds are established for the broadcast scenario.

Abstract

The channel synthesis problem has been widely investigated over the last decade. In this paper, we consider the sequential version in which the encoder and the decoder work in a sequential way. Under a mild assumption on the target joint distribution we provide a complete (single-letter) characterization of the solution for the point-to-point case, which shows that the canonical symbol-by-symbol mapping is not optimal in general, but is indeed optimal if we make some additional assumptions on the encoder and decoder. We also extend this result to the broadcast scenario and the interactive communication scenario. We provide bounds in the broadcast setting and a complete characterization of the solution under a mild condition on the target joint distribution in the interactive communication case. Our proofs are based on a R\'enyi entropy method.