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An entropy theorem for computing the capacity of weakly (d,k)-constrained sequences

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Abstract

We find an analytic expression for the maximum of the normalized entropy -Σ<sub>iεT</sub>p<sub>i</sub>ln p<sub>i</sub>/Σ<sub>iεT</sub>ip<sub>i</sub> where the set T is the disjoint union of sets S<sub>n</sub> of positive integers that are assigned probabilities P<sub>n</sub>, Σ<sub>n</sub>P<sub>n </sub>=1. This result is applied to the computation of the capacity of weakly (d,k)-constrained sequences that are allowed to violate the (d,k)-constraint with small probability

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Conference Paper
Upper and lower bounds are presented for the capacity of weakly constrained two-dimensional codes. The maximum entropy is calculated for two simple models of 2-D codes constraining the probability of neighboring 1s as an example. For given models of the coded data, upper and lower bounds on the capacity for 2-D channel models based on occurrences of neighboring 1s are considered.
Conference Paper
We find an analytic expression for the maximum of the normalized entropy -Σ<sub>i∈T</sub>p<sub>i</sub> ln p<sub>i</sub>/Σ<sub>i∈T</sub>ip<sub>i</sub> where the set T is the disjoint union of sets S<sub>n</sub> of positive integers that are assigned probabilities P<sub>n</sub>, Σ<sub>n</sub>P<sub>n </sub>=1. This result is applied to the computation of the capacity of weakly (d,k)-constrained sequences that are allowed to violate the (d,k)-constraint with small probability
Article
Full-text available
The author reports on the performance of a new class of constrained codes, called weakly constrained codes. These codes do not strictly guarantee the imposed channel constraints, but rather generate codewords that violate, with a given (small) probability, the prescribed constraint. Weakly constrained codes are specifically of interest when it is desirable that the code rate R=p/q is very high, requiring codewords of length q>100
Article
Bell System Technical Journal, also pp. 623-656 (October)
Associate Editor for Coding theory. Publisher Item Identifier S
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communicated by R. M. Roth, Associate Editor for Coding theory. Publisher Item Identifier S 0018-9448(00)03101-1.
Constrained coding is a special kind of channel coding in which unconstrained user sequences are encoded into sequences that are required to satisfy certain hard constraints such as runlength limits
  • I Introduction
I. INTRODUCTION Constrained coding is a special kind of channel coding in which unconstrained user sequences are encoded into sequences that are required to satisfy certain hard constraints such as runlength limits [10], [14], [13]. Manuscript received December 29, 1998. J. J. Ashley is with Infineon Technologies, Santa Cruz, CA 95060 USA (e-mail: Jonathan.Ashley@infineon.com).
CA 95120 USA (e-mail: marcus@almaden.ibm.com)
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B. H. Marcus is with IBM Almaden Research Center, San Jose, CA 95120 USA (e-mail: marcus@almaden.ibm.com). communicated by R. M. Roth, Associate Editor for Coding theory. Publisher Item Identifier S 0018-9448(00)03101-1.