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State-Complexity Reduction for Convolutional Codes Using Trellis-Module Integration Masato TAJIMA Koji OKINO Takashi MIYAGOSHI Publication 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 Keyword: convolutional codes, code trellis, trellis-module integration, minimal trellis, trellis complexity, Full Text: PDF(286.4KB)>>
Summary: Assume that G(D) is a k0  n0 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. | ||||||||||
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