2000/05/30 by Joachim Rosenthal, Rosenthal, Joachim · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #37B10 #93B25 #94B10 #Cellular Automata and Applications #Computability, Logic, AI Algorithms #DNA and Biological Computing #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.math/0005281
openalex publication_date 2000/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The article reviews different definitions for a convolutional code which can be found in the literature. The algebraic differences between the definitions are worked out in detail. It is shown that bi-infinite support systems are dual to finite-support systems under Pontryagin duality. In this duality the dual of a controllable system is observable and vice versa. Uncontrollability can occur only if there are bi-infinite support trajectories in the behavior, so finite and half-infinite-support systems must be controllable. Unobservability can occur only if there are finite support trajectories in the behavior, so bi-infinite and half-infinite-support systems must be observable. It is shown that the different definitions for convolutional codes are equivalent if one restricts attention to controllable and observable codes.