NDLI: An efficient algorithm for constructing minimal trellises for codes over finite Abelian groups

Content Provider	IEEE Xplore Digital Library
Author	Vazirani, V.V. Saran, H. Rajan, B.S.
Copyright Year	1996
Description	Author affiliation: Coll. of Comput., Georgia Inst. of Technol., Atlanta, GA, USA (Vazirani, V.V.)
Abstract	We present an efficient algorithm for computing the minimal trellis for a group code over a finite Abelian group, given a generator matrix for the code. We also show how to compute a succinct representation of the minimal trellis for such a code, and present algorithms that use this information to efficiently compute local descriptions of the minimal trellis. This extends the work of Kschischang and Sorokine (1995), who handled the case of linear codes over fields. An important application of our algorithms is to the construction of minimal trellises for lattices. A key step in our work is handling codes over cyclic groups C/sub p//spl alpha/, where p is a prime. Such a code can be viewed as a submodule over the ring Z/sub p//spl alpha/. Because of the presence of zero-divisors in the ring, submodules do not share the useful properties of vector spaces. We get around this difficulty by restricting the notion of linear combination to p-linear combination, and introducing the notion of a p-generator sequence, which enjoys properties similar to that of a generator matrix for a vector space.
Starting Page	144
Ending Page	153
File Size	970429
Page Count	10
File Format	PDF
ISBN	0818675942
ISSN	02725428
DOI	10.1109/SFCS.1996.548473
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1996-10-14
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Linear code Decoding Modulation coding Lattices Vectors Block codes Educational institutions Computer science Modems Bandwidth
Content Type	Text
Resource Type	Article

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