1,734 research outputs found
MacWilliams Identities for Terminated Convolutional Codes
Shearer and McEliece [1977] showed that there is no MacWilliams identity for
the free distance spectra of orthogonal linear convolutional codes. We show
that on the other hand there does exist a MacWilliams identity between the
generating functions of the weight distributions per unit time of a linear
convolutional code C and its orthogonal code C^\perp, and that this
distribution is as useful as the free distance spectrum for estimating code
performance. These observations are similar to those made recently by
Bocharova, Hug, Johannesson and Kudryashov; however, we focus on terminating by
tail-biting rather than by truncation.Comment: 5 pages; accepted for 2010 IEEE International Symposium on
Information Theory, Austin, TX, June 13-1
A complete MacWilliams theorem for convolutional codes
© 2014 IEEE. In this paper, we prove a MacWilliams identity for the weight adjacency matrices based on the constraint codes of a convolutional code (CC) and its dual. Our result improves upon a recent result by Gluesing-Luerssen and Schneider, where the requirement of a minimal encoder is assumed. We can also establish the MacWilliams identity for the input-parity weight adjacency matrices of a systematic CC and its dual. Most importantly, we show that a type of Hamming weight enumeration functions of all codewords of a CC can be derived from the weight adjacency matrix, which thus provides a connection between these two very different notions of weight enumeration functions in the convolutional code literature. Finally, the relations between various enumeration functions of a CC and its dual are summarized in a diagram. This explains why no MacWilliams identity exists for the free-distance enumerators
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