Searching for high-rate convolutional codes via binary syndrome trellises

Authors:
Florian Hug;Irina E. Bocharova;Rolf Johannessen;Boris D. Kudryashov
Affiliations:
Dept. of Electrical and Information Technology, Lund University, Lund, Sweden;Dept. of Information Systems, St. Petersburg Univ. of Information Technologies, Mechanics and Optics, St. Petersburg, Russia;Dept. of Electrical and Information Technology, Lund University, Lund, Sweden;Dept. of Information Systems, St. Petersburg Univ. of Information Technologies, Mechanics and Optics, St. Petersburg, Russia
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Year:
2009

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Abstract

Rate R = (c-1)/c convolutional codes of constraint length ν can be represented by conventional syndrome trellises with a state complexity of s = ν or by binary syndrome trellises with a state complexity of s = ν or s = ν + 1, which corresponds to at most 2s states at each trellis level. It is shown that if the parity-check polynomials fulfill certain conditions, there exist binary syndrome trellises with optimum state complexity s = ν. The BEAST is modified to handle parity-check matrices and used to generate code tables for optimum free distance rate R = (c - 1)/c, c = 3, 4, 5, convolutional codes for conventional syndrome trellises and binary syndrome trellises with optimum state complexity. These results show that the loss in distance properties due to the optimum state complexity restriction for binary trellises is typically negligible.