Maximum entropy charge-constrained run-length codes

Abstract

The authors present a study of run-length-limiting codes that have a null at zero frequency or DC. The class of codes or sequences considered is specified by three parameters: (d, k, c). The first two constraints, d and k, put lower and upper bounds on the run-lengths, while the charge constraint, c, is responsible for the spectral null. A description of the combined (d, k, c) constraints, in terms of a variable length graph, and its adjacency matrix, A(D), are presented. The maximum entropy description of the constraint described by a run-length graph is presented as well as the power spectral density. The results are used to study several examples of (d, k, c) constraints. The eigenvalues and eigenvectors of the classes of (d, k=2c-1, c) and (d, k=d+1, c) constraints for (c=1,2,. . .), are shown to satisfy certain second-order recursive equations. These equations are solved using the theory of Chebyshev polynomials.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>