A Quasi-Uniform Approach to Characterizing the Boundary of the Almost Entropic Region

TL;DR

This paper introduces a novel approach using quasi-uniform random vectors to characterize the boundary of the almost entropic region, with implications for network coding and entropy region analysis.

Contribution

It presents a new method leveraging quasi-uniform vectors to analyze the entropy region boundary and assess inner bounds for three variables.

Findings

Looseness of known inner bounds established

Applicable to network coding design

Characterizes boundary of almost entropic region

Abstract

The convex closure of entropy vectors for quasi-uniform random vectors is the same as the closure of the entropy region. Thus, quasi-uniform random vectors constitute an important class of random vectors for characterizing the entropy region. Moreover, the one-to-one correspondence between quasi-uniform codes and quasi-uniform random vectors makes quasi-uniform random vectors of central importance for designing effective codes for communication systems. In this paper, we present a novel approach that utilizes quasi-uniform random vectors for characterizing the boundary of the almost entropic region. In particular, we use the notion of quasi-uniform random vectors to establish looseness of known inner bounds for the entropy vectors at the boundary of the almost entropic region for three random variables. For communication models such as network coding, our approach can be applied to design network codes from quasi-uniform entropy vectors.