Asymptotic Achievable Rate of Two-Dimensional Constraint Codes based on Column by Column Encoding

TL;DR

This paper introduces a column-by-column encoding scheme for 2D constraint codes, deriving a lower bound on the maximum achievable rate using graph theory, with evaluations for specific constraints.

Contribution

It presents a novel encoding method for 2D codes and establishes a graph-theoretic lower bound on their achievable rate, advancing understanding of 2D constraint coding.

Findings

Lower bound of maximum achievable rate derived

Graph theoretical analysis applied to 2D constraints

Evaluations for asymmetric and symmetric bit constraints

Abstract

In this paper, we propose a column by column encoding scheme suitable for two-dimensional (2D) constraint codes and derive a lower bound of its maximum achievable rate. It is shown that the maximum achievable rate is equal to the largest minimum degree of a subgraph of the maximal valid pair graph. A graph theoretical analysis to provide a lower bound of the maximum achievable rate is presented. For several 2D-constraints such as the asymmetric and symmetric non-isolated bit constraints, the values of the lower bound are evaluated.