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Some structural properties of convolutional codes over rings

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3 Author(s)
R. Johannesson ; Dept. of Inf. Technol., Lund Univ., Sweden ; Zhe-Xian Wan ; E. Wittenmark

Convolutional codes over rings have been motivated by phase-modulated signals. Some structural properties of the generator matrices of such codes are presented. Successively stronger notions of the invertibility of generator matrices are studied, and a new condition for a convolutional code over a ring to be systematic is given and shown to be equivalent to a condition given by Massey and Mittelholzer (1990). It is shown that a generator matrix that can be decomposed into a direct sum is basic, minimal, and noncatastrophic if and only if all generator matrices for the constituent codes are basic, minimal, and noncatastrophic, respectively. It is also shown that if a systematic generator matrix can be decomposed into a direct sum, then all generator matrices of the constituent codes are systematic, but that the converse does not hold. Some results on convolutional codes over Z(pe) are obtained

Published in:

IEEE Transactions on Information Theory  (Volume:44 ,  Issue: 2 )