Zero-error Slepian-Wolf Coding of Confined Correlated Sources with Deviation Symmetry

TL;DR

This paper introduces Matrix Partition Codes for zero-error Slepian-Wolf coding of correlated sources with deviation symmetry, generalizing previous Hamming source codes and establishing conditions for optimality.

Contribution

It extends previous Hamming codes to Matrix Partition Codes, providing a unified framework for efficient zero-error source coding with deviation symmetry.

Findings

Matrix Partition Codes generalize Hamming source codes.

Every perfect or linear-optimal code is a Matrix Partition Code.

Conditions for Matrix Partition Codes to be perfect or linear-optimal are provided.

Abstract

In this paper, we use linear codes to study zero-error Slepian-Wolf coding of a set of sources with deviation symmetry, where the sources are generalization of the Hamming sources over an arbitrary field. We extend our previous codes, Generalized Hamming Codes for Multiple Sources, to Matrix Partition Codes and use the latter to efficiently compress the target sources. We further show that every perfect or linear-optimal code is a Matrix Partition Code. We also present some conditions when Matrix Partition Codes are perfect and/or linear-optimal. Detail discussions of Matrix Partition Codes on Hamming sources are given at last as examples.