On Independence and Capacity of Multidimensional Semiconstrained Systems

TL;DR

This paper introduces a new formula for the capacity limit of multidimensional semiconstrained systems by generalizing independence entropy, providing tighter bounds and exact capacity in certain cases, with implications for systems like (0,k,p)-RLL.

Contribution

The paper generalizes independence entropy to semiconstrained systems and derives a new capacity formula, improving bounds and achieving exact capacity in specific multidimensional cases.

Findings

Derived a new capacity formula for multidimensional semiconstrained systems.

Provided asymptotically tight bounds for axial-product systems.

Improved the known bounds for (0,k,p)-RLL systems.

Abstract

We find a new formula for the limit of the capacity of certain sequences of multidimensional semiconstrained systems as the dimension tends to infinity. We do so by generalizing the notion of independence entropy, originally studied in the context of constrained systems, to the study of semiconstrained systems. Using the independence entropy, we obtain new lower bounds on the capacity of multidimensional semiconstrained systems in general, and $d$-dimensional axial-product systems in particular. In the case of the latter, we prove our bound is asymptotically tight, giving the exact limiting capacity in terms of the independence entropy. We show the new bound improves upon the best-known bound in a case study of $(0,k,p)$-RLL.