Maximum entropy charge-constrained run-length codes

Author

Kerpez, Kenneth J. ; Gallopoulos, Ayis ; Heegard, Chris

Author_Institution

Bellcore, Morristown, NJ, USA

Volume

10

Issue

1

fYear

1992

fDate

1/1/1992 12:00:00 AM

Firstpage

242

Lastpage

253

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

Keywords

codes; eigenvalues and eigenfunctions; information theory; polynomials; Chebyshev polynomials; DC; adjacency matrix; charge constrained run length codes; charge constraint; eigenvalues; eigenvectors; lower bounds; maximum entropy; power spectral density; run length graph; run length limiting codes; second-order recursive equations; spectral null; upper bounds; variable length graph; zero frequency null; Chebyshev approximation; Closed-form solution; Constraint theory; Eigenvalues and eigenfunctions; Entropy; Equations; Frequency; Polynomials; Upper bound;

fLanguage

English

Journal_Title

Selected Areas in Communications, IEEE Journal on

Publisher

ieee

ISSN

0733-8716

Type

jour

DOI

10.1109/49.124483

Filename

124483