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System-theoretic properties of convolutional codes over rings. (English) Zbl 1028.94033

Convolutional codes over rings are particularly suitable for representing codes over phase-modulation signals. In order to develop a complete structural analysis of this class of codes, it is necessary to study rational matrices over rings, which constitutes the generator matrices (encoders) for such convolutional codes. Noncatastrophic, minimal systematic, and basic generator matrices are introduced and characterized by using a canonical form for polynomial matrices over rings. Finally, some classes of convolutional codes, defined according to the generator matrix they admit, are introduced and analyzed from a system-theoretic point of view.

MSC:

94B10 Convolutional codes
15B33 Matrices over special rings (quaternions, finite fields, etc.)
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