State-Complexity Reduction for Convolutional Codes Using Trellis-Module Integration

Masato TAJIMA  Koji OKINO  Takashi MIYAGOSHI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.10   pp.2466-2474
Publication Date: 2006/10/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.10.2466
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coding Theory
convolutional codes,  code trellis,  trellis-module integration,  minimal trellis,  trellis complexity,  

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Assume that G(D) is a k0n0 canonical generator matrix. Let G(L)(D) be the generator matrix obtained by integrating L consecutive trellis-modules associated with G(D). We also consider a modified version of G(L)(D) using a column permutation. Then take notice of the corresponding minimal trellis-module T(L). In this paper, we show that there is a case where the minimum number of states over all levels in T(L) is less than the minimum attained for the minimal trellis-module associated with G(D). In this case, combining with a shifted sectionalization of the trellis, we can construct a trellis-module with further reduced number of states. We actually present such an example. We also clarify the mechanism of state-space reduction. That is, we show that trellis-module integration combined with an appropriate column permutation and a shifted sectionalization of the trellis is equivalent to shifting some particular bits of the original code bits by L time units.