DocumentCode :
771526
Title :
Time-Varying Maximum Transition Run Constraints
Author :
Poo, T. Lei ; Marcus, Brian H.
Author_Institution :
Dept. of Electr. Eng., Stanford Univ., CA
Volume :
52
Issue :
10
fYear :
2006
Firstpage :
4464
Lastpage :
4480
Abstract :
Maximum transition run (MTR) constrained systems are used to improve detection performance in storage channels. Recently, there has been a growing interest in time-varying MTR (TMTR) systems, after such codes were observed to eliminate certain error events and thus provide high coding gain for EnPR4 channels for n=2,3. In this work, TMTR constraints parameterized by a vector, whose coordinates specify periodically the maximum runlengths of 1´s ending at the positions, are investigated. A canonical way to classify such constraints and simplify their minimal graph presentations is introduced. It is shown that there is a particularly simple presentation for a special class of TMTR constraints and explicit descriptions of their characteristic equations are derived. New upper bounds on the capacity of TMTR constraints are established, and an explicit linear ordering by capacity of all tight TMTR constraints up to period 4 is given. For MTR constrained systems with unconstrained positions, it is shown that the set of sequences restricted to the constrained positions yields a natural TMTR constraint. Using TMTR constraints, a new upper bound on the tradeoff function for MTR systems that relates the density of unconstrained positions to the maximum code rates is determined
Keywords :
graph theory; runlength codes; sequences; telecommunication channels; time-varying systems; TMTR; graph presentation; maximum runlength; maximum transition run constrained system; sequence; storage channel; time-varying MTR system; Australia; Equations; Error analysis; Information retrieval; Information theory; Magnetic recording; Pattern analysis; Semiconductor materials; Time varying systems; Upper bound; Capacity; constrained systems; maximum transition run (MTR); time varying; tradeoff function; upper bounds;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.2006.881706
Filename :
1705006
Link To Document :
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