Remote Channel Synthesis

TL;DR

This paper characterizes the optimal rates for synthesizing a remote channel with partial observations, revealing that standard schemes are sub-optimal when common randomness is limited, especially for joint distributions that are not product distributions.

Contribution

It provides a single-letter characterization of the minimal rates for compression and common randomness in remote channel synthesis, highlighting the limitations of standard schemes under certain conditions.

Findings

Optimal rates for remote channel synthesis are characterized.

Standard channel synthesis schemes are sub-optimal with limited common randomness.

Joint distributions that are not product distributions require more sophisticated schemes.

Abstract

We consider the problem of synthesizing a memoryless channel between an unobserved source and a remote terminal. An encoder has access to a partial or noisy version $Z^n = (Z_1, \ldots, Z_n)$ of a remote source sequence $X^n = (X_1, \ldots, X_n),$ with $(X_i,Z_i)$ independent and identically distributed with joint distribution $q_{X,Z}.$ The encoder communicates through a noiseless link to a decoder which aims to produce an output $Y^n$ coordinated with the remote source; that is, the total variation distance between the joint distribution of $X^n$ and $Y^n$ and some i.i.d. target distribution $q_{X,Y}^{\otimes n}$ is required to vanish as $n$ goes to infinity. The two terminals may have access to a source of rate-limited common randomness. We present a single-letter characterization of the optimal compression and common randomness rates. We also show that when the common randomness rate is small, then in most cases, coordinating $Z^n$ and $Y^n$ using a standard channel synthesis scheme is strictly sub-optimal. In other words, schemes for which the joint distribution of $Z^n$ and $Y^n$ approaches a product distribution asymptotically are strictly sub-optimal.