MacWilliams Identities for Terminated Convolutional Codes

Details MacWilliams Identities for Terminated Convolutional Codes MacWilliams Identities for Terminated Convolutional Codes

2010-01-05

arxiv.org/abs/1001.0723v3

Computer Science

Information Theory

5 pages; accepted for 2010 IEEE International Symposium on Information Theory, Austin, TX, June 13-18

Scientific paper

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.

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