On the Sub-optimality of Single-letter Coding in Multi-terminal Communications

TL;DR

This paper analyzes binary block-codes generated with single-letter distributions, demonstrating their sub-optimality in certain multi-terminal communication scenarios through spectral dependency bounds.

Contribution

It characterizes the dependency spectrum of randomly generated BBCs and proves the sub-optimality of large blocklength single-letter coding schemes in some multiterminal settings.

Findings

Single-letter coding schemes are sub-optimal in some multiterminal communication settings.

Dependency spectrum bounds limit correlation between distributed BBC outputs.

Large blocklength schemes do not always achieve optimal performance.

Abstract

We investigate binary block-codes (BBC). A BBC is defined as a vector of Boolean functions. We consider BBCs which are generated randomly, and using single-letter distributions. We characterize the vector of dependency spectrums of these BBCs. We use this vector to upper-bound the correlation between the outputs of two distributed BBCs. Finally, the upper-bound is used to show that the large blocklength single-letter coding schemes in the literature are sub-optimal in some multiterminal communication settings.