Broadcast Channel Synthesis from Shared Randomness

TL;DR

This paper investigates how to synthesize a two-user broadcast channel using shared randomness and communication, providing bounds on the tradeoff between communication rate and shared randomness, with some bounds being tight in special cases.

Contribution

It introduces new inner and lower bounds on the tradeoff region for broadcast channel synthesis with shared randomness, extending previous work.

Findings

Bounds are tight for certain special cases.

Provides an inner bound on the tradeoff between communication and shared randomness.

Establishes a lower bound on the minimum communication rate.

Abstract

We study the problem of synthesising a two-user broadcast channel using a common message, where each output terminal shares an independent source of randomness with the input terminal. This generalises two problems studied in the literature (Cuff, IEEE Trans. Inform. Theory, 2013; Kurri et.al., IEEE Trans. Inform. Theory, 2021). We give an inner bound on the tradeoff region between the rates of communication and shared randomness, and a lower bound on the minimum communication rate. Although the bounds presented here are not tight in general, they are tight for some special cases, including the aforementioned problems.