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IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 2006 E89-A(10):2466-2474; doi:10.1093/ietfec/e89-a.10.2466
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Copyright © 2006 The Institute of Electronics, Information and Communication Engineers

Special Section on Information Theory and Its Applications -- Papers -- Coding Theory

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

Masato TAJIMA1, Koji OKINO2 and Takashi MIYAGOSHI1

1 The authors are with the Department of Intellectual Information Systems Engineering, University of Toyama, Toyama-shi, 930-8555 Japan. E-mail: tajima{at}eng.u-toyama.ac.jp, miyagosi{at}eng.u-toyama.ac.jp, 2 The author is with the Information Technology Center, University of Toyama, Toyama-shi, 930-8555 Japan. E-mail: okino{at}itc.u-toyama.ac.jp

Assume that G(D) is a k0xn0 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.

Key Words: convolutional codes, code trellis, trellis-module integration, minimal trellis, trellis complexity

Manuscript received January 10, 2006. Manuscript revised April 15, 2006. Final manuscript received May 23, 2006.


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