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

Publication: Research - peer-review › Journal article – Annual report year: 2007

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**Entropy of Bit-Stuffing-Induced Measures for Two-Dimensional Checkerboard Constraints.** / Forchhammer, Søren; Vaarby, Torben Strange.

Publication: Research - peer-review › Journal article – Annual report year: 2007

### Harvard

*I E E E Transactions on Information Theory*, vol 53, no. 4, pp. 1537-1546., 10.1109/TIT.2007.892781

### APA

*I E E E Transactions on Information Theory*,

*53*(4), 1537-1546. 10.1109/TIT.2007.892781

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*I E E E Transactions on Information Theory*. 2007, 53(4). 1537-1546. Available: 10.1109/TIT.2007.892781

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### RIS

TY - JOUR

T1 - Entropy of Bit-Stuffing-Induced Measures for Two-Dimensional Checkerboard Constraints

AU - Forchhammer,Søren

AU - Vaarby,Torben Strange

PB - I E E E

N1 - 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.

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - run-length-limited (RLL) constraints

KW - bit-stuffing encoding

KW - 2-D constraints

KW - cascading two-dimensional (2-D) arrays

U2 - 10.1109/TIT.2007.892781

DO - 10.1109/TIT.2007.892781

JO - I E E E Transactions on Information Theory

JF - I E E E Transactions on Information Theory

SN - 0018-9448

IS - 4

VL - 53

SP - 1537

EP - 1546

ER -