Math @ Duke

Publications [#235758] of Robert Calderbank
Papers Published
 Calderbank, AB; Forney, GD; Vardy, A, Minimal tailbiting trellises: The Golay code and more,
IEEE International Symposium on Information Theory  Proceedings
(December, 1998),
pp. 255, ISSN 21578095 [doi]
(last updated on 2017/12/14)
Abstract: A 16state tailbiting trellis for the binary (24,12,8) Golay code C 24 is exhibited. This tailbiting trellis is minimal. It has many other nice properties, and may be simpler to decode than the minimal conventional trellis for C 24 . Unwrapping this tailbiting trellis produces a periodicallytimevarying 16state rate1/2 convolutional code. This «Golay convolutional code» is the first known example of a selfdual doublyeven binary linear convolutional code. It has greater minimum distance than any 16state timeinvariant convolutional code of rate 1/2. Demonstrably minimal tailbiting trellises are given for several other binary and nonbinary selfdual codes. For some nonbinary codes, tailbiting trellises based on code generators over a group are simpler than any tailbiting trellis based on linear generators over a field. © 1998 IEEE.


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