A Graph Representation for Two-Dimensional Finite Type Constrained Systems

TL;DR

This paper introduces a novel graph representation for two-dimensional finite type constrained systems, enabling better analysis and generation of constrained blocks, which addresses a key challenge in two-dimensional source coding.

Contribution

The paper proposes the first graph representation for two-dimensional finite type constrained systems, facilitating analysis and element generation.

Findings

Graph representation effectively models two-dimensional constraints.

Method enables systematic generation of constrained blocks.

Addresses open problems in two-dimensional source coding.

Abstract

The demand of two-dimensional source coding and constrained coding has been getting higher these days, but compared to the one-dimensional case, many problems have remained open as the analysis is cumbersome. A main reason for that would be because there are no graph representations discovered so far. In this paper, we focus on a two-dimensional finite type constrained system, a set of two-dimensional blocks characterized by a finite number of two-dimensional constraints, and propose its graph representation. We then show how to generate an element of the two-dimensional finite type constrained system from the graph representation.