TY - GEN

T1 - Constrained codes as networks of relations

AU - Schwartz, Moshe

AU - Bruck, Jehoshua

PY - 2007/12/1

Y1 - 2007/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=51649126441&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2007.4557416

DO - 10.1109/ISIT.2007.4557416

M3 - Conference contribution

AN - SCOPUS:51649126441

SN - 1424414296

SN - 9781424414291

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1386

EP - 1390

BT - Proceedings - 2007 IEEE International Symposium on Information Theory, ISIT 2007

T2 - 2007 IEEE International Symposium on Information Theory, ISIT 2007

Y2 - 24 June 2007 through 29 June 2007

ER -