Hash Property and Fixed-rate Universal Coding Theorems

TL;DR

This paper demonstrates that fixed-rate universal coding problems can be achieved using hash properties, specifically by employing sparse matrices that satisfy these properties, advancing universal coding theory.

Contribution

It introduces the use of hash property and sparse matrices to construct fixed-rate universal codes, providing a new approach to universal source and channel coding.

Findings

Sparse matrices satisfy the hash property requirement.

Universal codes can be constructed using sparse matrices.

Achievability of fixed-rate universal coding is proven.

Abstract

The aim of this paper is to prove the achievability of fixed-rate universal coding problems by using our previously introduced notion of hash property. These problems are the fixed-rate lossless universal source coding problem and the fixed-rate universal channel coding problem. Since an ensemble of sparse matrices satisfies the hash property requirement, it is proved that we can construct universal codes by using sparse matrices.