On the Structure of Real-Time Encoders and Decoders in a Multi-Terminal Communication System

TL;DR

This paper analyzes the structure of optimal real-time encoders and decoders in a multi-terminal communication system with noisy channels, revealing finite-dimensional sufficient statistics and a new methodology for noiseless channels.

Contribution

It introduces a novel approach to determine the structure of real-time encoders and decoders, including finite-dimensional sufficient statistics under specific Markov assumptions.

Findings

Existence of finite-dimensional sufficient statistics for encoders.

A new methodology for structure analysis using common information.

Time-invariant sufficient statistic for noiseless channels.

Abstract

A real-time communication system with two encoders communicating with a single receiver over separate noisy channels is considered. The two encoders make distinct partial observations of a Markov source. Each encoder must encode its observations into a sequence of discrete symbols. The symbols are transmitted over noisy channels to a finite memory receiver that attempts to reconstruct some function of the state of the Markov source. Encoding and decoding must be done in real-time, that is, the distortion measure does not tolerate delays. Under the assumption that the encoders' observations are conditionally independent Markov chains given an unobserved time-invariant random variable, results on the structure of optimal real-time encoders and the receiver are obtained. It is shown that there exist finite-dimensional sufficient statistics for the encoders. The problem with noiseless channels and perfect memory at the receiver is then considered. A new methodology to find the structure of optimal real-time encoders is employed. A sufficient statistic with a time-invariant domain is found for this problem. This methodology exploits the presence of common information between the encoders and the receiver when communication is over noiseless channels.