Constrained Codes as Networks of Relations

Abstract

We revisit the well-known problem of determining the capacity of constrained systems. While the one-dimensional case is well understood, the capacity of two-dimensional systems is mostly unknown. When it is non-zero, except for the (1,∞ )- RLL system on the hexagonal lattice, there are no closed-form analytical solutions known. Furthermore, for the related problem of counting the exact number of constrained arrays of any given size, only exponential-time algorithms are known. We present a novel approach to finding the exact capacity of two-dimensional constrained systems, as well as efficiently counting the exact number of constrained arrays of any given size. To that end, we borrow graph-theoretic tools originally developed for the field of statistical mechanics, tools for efficiently simulating quantum circuits, as well as tools from the theory of the spectral distribution of Toeplitz matrices.

Files

Additional details