A MacWilliams Identity for Convolutional Codes: The General Case
Heide Gluesing-Luerssen, Gert Schneider
TL;DR
This paper establishes a general MacWilliams Identity for convolutional codes using weight adjacency matrices derived from state space realizations, applicable to various duality notions in convolutional coding theory.
Contribution
It introduces a unified MacWilliams Identity for convolutional codes based on weight adjacency matrices and state space realizations, extending previous results to a broader context.
Findings
Derives a MacWilliams Identity for convolutional codes using weight adjacency matrices.
Applies the identity to various notions of duality in convolutional coding.
Provides a theoretical framework connecting code duality and weight distributions.
Abstract
A MacWilliams Identity for convolutional codes will be established. It makes use of the weight adjacency matrices of the code and its dual, based on state space realizations (the controller canonical form) of the codes in question. The MacWilliams Identity applies to various notions of duality appearing in the literature on convolutional coding theory.
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Taxonomy
TopicsError Correcting Code Techniques · Cellular Automata and Applications · Advanced Wireless Communication Techniques