NDLI: Zero/positive capacities of two-dimensional runlength constrained arrays

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Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252)

Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252)

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2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060)

Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252)

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Proceedings. 1991 IEEE International Symposium on Information Theory

1988 IEEE International Symposium on Information Theory.

Zero/positive capacities of two-dimensional runlength constrained arrays

Content Provider	IEEE Xplore Digital Library
Author	Etzion, T. Paterson, K.G.
Copyright Year	2001
Description	Author affiliation: Dept. of Comput. Sci., Technion-Israel Inst. of Technol., Haifa, Israel (Etzion, T.)
Abstract	A binary sequence satisfies a one-dimensional (d, k) runlength constraint if every run of zeroes has length at least d and at most k. A binary sequence satisfies a one-dimensional (d/sub 1/, k/sub 1/, d/sub 2/, k/sub 2/) runlength constraint if every run of zeroes has length at least d/sub 1/ and at most k/sub 2/ and every run of ones has length at least d/sub 2/ and at most k/sub 2/. A two-dimensional binary array is said to satisfy a (d/sub 1/, k/sub 1/, d/sub 2/, k/sub 2/; d/sub 3/, d/sub 4/, k/sub 4/) runlength constraint if it satisfies the one-dimensional (d/sub 1/, k/sub 1/, d/sub 2/, k/sub 2/) runlength constraint horizontally (i.e. on every row) and the one-dimensional (d/sub 3/, k/sub 3/, d/sub 4/, k/sub 4/) runlength constraint vertically (i.e. on every column). For convenience, we will say that a binary array satisfies the (d,k) runlength constraint if each row and each column satisfy the (d,k) runlength constraint and that a binary array satisfies the (d/sub 1/, k/sub 1/, d/sub 2/, k/sub 2/) runlength constraint if it is (d/sub 1/, k/sub 1/, d/sub 2/, k/sub 2/) runlength constrained both horizontally and vertically. We say that a binary array satisfies the (d/sub 1/, k/sub 1/; d/sub 3/, k/sub 3/) runlength constraint if each row satisfies the (d/sub 1/, k/sub 1/, d/sub 1/, k/sub 1/) runlength constraint and each column satisfies the (d/sub 3/, k/sub 3/, d/sub 3/, k/sub 3/) runlength constraint. Finally, we always allow violation of the smallest runlength constraint at the beginning and the end sequences and at the edges of arrays. In this work we examine the following basic question: for which values of d/sub 1/, k/sub 1/, d/sub 2/, k/sub 2/, d/sub 3/, k/sub 3/, d/sub 4/, k/sub 4/, is C(d/sub 1/, k/sub 1/, d/sub 2/, k/sub 2/; d/sub 3/, k/sub 3/, d/sub 4/, k/sub 4/) positive and for which values is it equal to zero?.
Sponsorship	IEEE Inf. Theory Soc
File Size	241404
File Format	PDF
ISBN	0780371232
DOI	10.1109/ISIT.2001.936132
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2001-06-29
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Binary sequences
Content Type	Text
Resource Type	Article

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