Some structural properties of convolutional codes over rings

Rolf Johannesson, Zhe-Xian Wan, Emma Wittenmark

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Abstract

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
Original languageEnglish
Pages (from-to)839-845
JournalIEEE Transactions on Information Theory
Volume44
Issue number2
DOIs
Publication statusPublished - 1998

Subject classification (UKÄ)

  • Electrical Engineering, Electronic Engineering, Information Engineering

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