Local Irreducibility of Tail-Biting Trellises

This paper investigates tail-biting trellis realizations for linear block codes. Intrinsic trellis properties are used to characterize irreducibility on given intervals of the time axis. It proves beneficial to always consider the trellis and its dual simultaneously. A major role is played by trelli...

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Bibliographic Details
Published in:IEEE transactions on information theory 2013-10, Vol.59 (10), p.6597-6610
Main Authors: Gluesing-Luerssen, Heide, Forney, G. David
Format: Article
Language:English
Subjects:
Applied sciences
Block codes
Codes
Codes on graphs
Coding, codes
Complexity theory
Controllability
duality
Exact sciences and technology
Generators
Indexes
Information theory
Information, signal and communications theory
Merging
minimality
Signal and communications theory
Telecommunications and information theory
Trajectory
trellis fragments
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Summary:This paper investigates tail-biting trellis realizations for linear block codes. Intrinsic trellis properties are used to characterize irreducibility on given intervals of the time axis. It proves beneficial to always consider the trellis and its dual simultaneously. A major role is played by trellis properties that amount to observability and controllability of trellis fragments of various lengths. For fragments of length less than the minimum span length of the code it is shown that fragment observability and fragment controllability are equivalent to irreducibility. For reducible trellises, a constructive reduction procedure is presented. The considerations also lead to a characterization for when the dual of a trellis allows a product factorization into elementary ("atomic") trellises.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2013.2267612