NDLI: Maximizing the Shannon Capacity of Constrained Systems with Two Constraints

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Maximizing the Shannon Capacity of Constrained Systems with Two Constraints

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Kashyap, Navin
Copyright Year	2003
Abstract	In this paper, we consider the problem of finding the set $\{A,B\} \subset {0,1}m that maximizes, among all 2-subsets of ${\{0,1\}}^m$, the Shannon capacity, H(A,B), of a constrained system of binary sequences that do not contain A or B as a contiguous subsequence. This problem is motivated by the problem of finding a pair of length-m binary sequences, called markers, that achieves the maximum rate, R(2,m,n), of a (2,m,n) periodic prefix-synchronized (PPS) code. A (2,m,n) PPS code is a binary block code with two length-m markers, A,B, and codewords of length n that inserts A and B alternately at regular intervals in the encoded bitstream, with the additional constraint that A and B may not appear anywhere in the encoded bitstream other than where inserted. We show that for any $m \geq 2$, $\lim_{n \rightarrow \infty} R(2,m,n) = \max\{H(A,B): \{A,B\} \subset {\{0,1\}}^m\} = \log_2\rho_{m-1}$, where $\rho_{m-1}$ is the largest-magnitude zero of the polynomial $z^{m-1} - z^{m-2} - \cdots - 1$. Moreover, we completely characterize the sequences A and B that achieve $\max H(A,B), as well as those that achieve R(2,m,n) for all sufficiently large n.
Starting Page	298
Ending Page	319
Page Count	22
File Format	PDF
ISSN	08954801
DOI	10.1137/S0895480102402757
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	2
Volume Number	17
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-01
Access Restriction	Subscribed
Subject Keyword	Symbolic dynamics Coding and information theory periodic prefix-synchronized codes constrained codes Shift register sequences and sequences over finite alphabets Shannon capacity Prefix, length-variable, comma-free codes shifts of finite type
Content Type	Text
Resource Type	Article
Subject	Mathematics

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