The capacity of finite Abelian group codes over symmetric memoryless channels
IEEE Transactions on Information Theory
A MacWilliams identity for convolutional codes: the general case
IEEE Transactions on Information Theory
Decoding of high rate convolutional codes using the dual trellis
IEEE Transactions on Information Theory
Group codes outperform binary-coset codes on nonbinary symmetric memoryless channels
IEEE Transactions on Information Theory
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Fundamental results concerning the dynamics of abelian group codes (behaviors) and their duals are developed. Duals of sequence spaces over locally compact abelian (LCA) groups may be defined via Pontryagin duality; dual group codes are orthogonal subgroups of dual sequence spaces. The dual of a complete code or system is finite, and the dual of a Laurent code or system is (anti-)Laurent. If C and C⊥ are dual codes, then the state spaces of C act as the character groups of the state spaces of C⊥. The controllability properties of C are the observability properties of C⊥. In particular, C is (strongly) controllable if and only if C⊥ is (strongly) observable, and the controller memory of C is the observer memory of C⊥. The controller granules of C act as the character groups of the observer granules of C⊥. Examples of minimal observer-form encoder and syndrome-former constructions are given. Finally, every observer granule of C is an "end-around" controller granule of C.