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

Søren Forchhammer, Torben Strange Vaarby

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    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
    Issue number4
    Pages (from-to)1537-1546
    Publication statusPublished - 2007

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


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