Channel Coding and Lossy Source Coding Using a Constrained Random Number Generator

TL;DR

This paper introduces stochastic encoders for channel and lossy source coding using constrained random number generators, achieving rates close to theoretical limits with practical encoding and decoding methods.

Contribution

It proposes a novel stochastic encoding scheme based on constrained random numbers and extends the hash property to general channels and sources.

Findings

Achieves rates near fundamental limits for channel and source coding.

Uses sparse matrices and sum-product algorithm for practical encoding/decoding.

Extends theoretical results to general channels and sources.

Abstract

Stochastic encoders for channel coding and lossy source coding are introduced with a rate close to the fundamental limits, where the only restriction is that the channel input alphabet and the reproduction alphabet of the lossy source code are finite. Random numbers, which satisfy a condition specified by a function and its value, are used to construct stochastic encoders. The proof of the theorems is based on the hash property of an ensemble of functions, where the results are extended to general channels/sources and alternative formulas are introduced for channel capacity and the rate-distortion region. Since an ensemble of sparse matrices has a hash property, we can construct a code by using sparse matrices, where the sum-product algorithm can be used for encoding and decoding by assuming that channels/sources are memoryless.