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Content Provider | IEEE Xplore Digital Library |
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Author | Ashley, J.J. Karabed, R. Siegel, P.H. |
Copyright Year | 1963 |
Abstract | A constrained system, or sofic system, S is the set of symbol strings generated by the finite-length paths through a finite labeled, directed graph. Karabed and Marcus (1988), extending the work of Adler, Coppersmith, and Hassner (1983), used the technique of state-splitting to prove the existence of a noncatastrophic, rate p:q finite-state encoder from binary data into S for any input word length p and codeword length q satisfying p/q/spl les/cap(S), the Shannon (1948) capacity. For constrained systems that are almost-finite-type, they further proved the existence of encoders enjoying a stronger form of decodability-namely, sliding-block decodability. In particular, their result implies the existence of a 100% efficient (rate 1/2), sliding-block code for the charge-constrained, runlength-limited constraint with parameters (d, k; c)=(1,3; 3), an almost-finite-type system with capacity precisely 1/2. We describe two quite different constructions of such codes. The constructions highlight connections between the problem of determining sliding-block decodability of a finite-state encoder and certain problems of colorability for graphs and sets. Using these connections, we show that the problem of determining the existence of a block-decodable input tag assignment for a given rate p:q, finite-state encoder is NP-complete, for p>1. We also prove NP-completeness results for several related problems in combinatorics and coding. |
Sponsorship | IEEE Information Theory Society |
Starting Page | 1925 |
Ending Page | 1947 |
Page Count | 23 |
File Size | 2505104 |
File Format | |
ISSN | 00189448 |
Volume Number | 42 |
Issue Number | 6 |
Language | English |
Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
Publisher Date | 1996-11-01 |
Publisher Place | U.S.A. |
Access Restriction | Subscribed |
Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
Subject Keyword | Decoding Combinatorial mathematics Digital modulation Modulation coding Digital recording Frequency Constraint theory Information theory Semiconductor device noise Q measurement |
Content Type | Text |
Resource Type | Article |
Subject | Computer Science Applications Library and Information Sciences Information Systems |
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