Entropy of Bit-Stuffing-Induced Measures for Two-Dimensional Checkerboard Constraints

Søren Forchhammer, Torben Strange Vaarby

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    Abstract

    A modified bit-stuffing scheme for two-dimensional (2-D) checkerboard constraints is introduced. The entropy of the scheme is determined based on a probability measure defined by the modified bit-stuffing. Entropy results of the scheme are given for 2-D constraints on a binary alphabet. The constraints considered are 2-D RLL (d, infinity) for d = 2, 3 and 4 as well as for the constraint with a minimum 1-norm distance of 3 between Is. For these results the entropy is within 1-2% of an upper bound on the capacity for the constraint. As a variation of the scheme, periodic merging arrays are also considered.
    Original languageEnglish
    JournalI E E E Transactions on Information Theory
    Volume53
    Issue number4
    Pages (from-to)1537-1546
    ISSN0018-9448
    DOIs
    Publication statusPublished - 2007

    Bibliographical note

    Copyright 2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

    Keywords

    • run-length-limited (RLL) constraints
    • bit-stuffing encoding
    • 2-D constraints
    • cascading two-dimensional (2-D) arrays

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