A Systems Theory Approach to Periodically Time-Varying Convolutional Codes by Means of Their Invariant Equivalent
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- Climent JJ., Herranz V., Perea C., Tomás V. (2009) A Systems Theory Approach to Periodically Time-Varying Convolutional Codes by Means of Their Invariant Equivalent. In: Bras-Amorós M., Høholdt T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2009. Lecture Notes in Computer Science, vol 5527. Springer, Berlin, Heidelberg
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.
KeywordsTime-varying convolutional codes controllability observability free distance
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