The capacity of finite Abelian group codes over symmetric memoryless channels
IEEE Transactions on Information Theory
On minimality of convolutional ring encoders
IEEE Transactions on Information Theory
A study on new right/left inverses of nonsquare polynomial matrices
International Journal of Applied Mathematics and Computer Science - SPECIAL SECTION: Efficient Resource Management for Grid-Enabled Applications
| Hi-index | 754.96 |
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