Tailbiting codes: Bounds and search results

Irina Bocharova, Rolf Johannesson, Boris Kudryashov, Per Ståhl

Research output: Contribution to journalArticlepeer-review

22 Citations (SciVal)


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.
Original languageEnglish
Pages (from-to)137-148
JournalIEEE Transactions on Information Theory
Issue number1
Publication statusPublished - 2002

Subject classification (UKÄ)

  • Electrical Engineering, Electronic Engineering, Information Engineering


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


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