Bounds on the Rate of 2-D Bit-Stuffing Encoders

TL;DR

This paper introduces a linear programming approach to bound the rate of 2-D bit-stuffing encoders using quasi-stationary properties, providing tighter bounds and insights into the capacity of 2-D constraints.

Contribution

It develops a novel method employing linear programs based on quasi-stationary properties to bound encoder rates and capacities for 2-D constraints.

Findings

Tighter lower bounds on encoder rates for certain constraints.

Bounds are derived from linear programming formulations.

Lower bounds on encoder rate also serve as lower bounds on capacity.

Abstract

A method for bounding the rate of bit-stuffing encoders for 2-D constraints is presented. Instead of considering the original encoder, we consider a related one which is quasi-stationary. We use the quasi-stationary property in order to formulate linear requirements that must hold on the probabilities of the constrained arrays that are generated by the encoder. These requirements are used as part of a linear program. The minimum and maximum of the linear program bound the rate of the encoder from below and from above, respectively. A lower bound on the rate of an encoder is also a lower bound on the capacity of the corresponding constraint. For some constraints, our results lead to tighter lower bounds than what was previously known.