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StateComplexity Reduction for Convolutional Codes Using TrellisModule Integration
Masato TAJIMA Koji OKINO Takashi MIYAGOSHI
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E89A
No.10
pp.24662474 Publication Date: 2006/10/01
Online ISSN: 17451337
DOI: 10.1093/ietfec/e89a.10.2466
Print ISSN: 09168508 Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications) Category: Coding Theory Keyword: convolutional codes, code trellis, trellismodule integration, minimal trellis, trellis complexity,
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Summary:
Assume that G(D) is a k_{0}n_{0} canonical generator matrix. Let G^{(L)}(D) be the generator matrix obtained by integrating L consecutive trellismodules 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 trellismodule 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 trellismodule associated with G(D). In this case, combining with a shifted sectionalization of the trellis, we can construct a trellismodule with further reduced number of states. We actually present such an example. We also clarify the mechanism of statespace reduction. That is, we show that trellismodule 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.

