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Tailbiting codes: Bounds and search results

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Author

Summary, in English

Tailbiting trellis representations of linear block codes with an arbitrary sectionalization of the time axis are studied. The notations of regular and irregular tailbiting codes are introduced and their maximal state complexities are lower-bounded. The asymptotic behavior of the derived bound is investigated. Furthermore, for regular tailbiting codes the product state complexity is lower-bounded. Tables of new tailbiting trellis representations of linear block codes of rates 1/2, 1/3, and 1/4 are presented. Almost all found trellises are optimal in the sense of the new bound on the state complexity and for most codes with nonoptimal trellises there exist time-varying trellises which are optimal. Five of our newly found tailbiting codes are better than the previously known linear codes with the same parameters. Four of them are also superior to any previously known nonlinear code with the same parameters. Also, more than 40 other quasi-cyclic codes have been found that improve the parameter set of previously known quasi-cyclic codes.

Publishing year

2002

Language

English

Pages

137-148

Publication/Series

IEEE Transactions on Information Theory

Volume

48

Issue

1

Document type

Journal article

Publisher

IEEE - Institute of Electrical and Electronics Engineers Inc.

Topic

  • Electrical Engineering, Electronic Engineering, Information Engineering

Keywords

  • asymptotic complexity bounds
  • state complexity
  • tailbiting codes
  • trellis
  • quasi-cyclic codes

Status

Published

ISBN/ISSN/Other

  • ISSN: 0018-9448