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Published in:
2009 | OriginalPaper | Chapter
A Systems Theory Approach to Periodically Time-Varying Convolutional Codes by Means of Their Invariant Equivalent
Authors : Joan-Josep Climent, Victoria Herranz, Carmen Perea, Virtudes Tomás
Published in: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Publisher: Springer Berlin Heidelberg
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In this paper we construct (
n
,
k
,
δ
) time-variant convolutional codes of period
τ
. We use the systems theory to represent our codes by the input-state-output representation instead of using the generator matrix. The obtained code is controllable and observable. This construction generalizes the one proposed by Ogasahara, Kobayashi, and Hirasawa (2007). We also develop and study the properties of the time-invariant equivalent convolutional code and we show a lower bound for the free distance in the particular case of MDS block codes.