An E cient Algorithm for Constructing Minimal Trellises for Codes over Finite Abelian Groups
نویسندگان
چکیده
We present an eecient algorithm for computing the minimal trellis for a group code over a nite 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 eeciently compute local descriptions of the minimal trellis. This extends the work of Kschischang and Sorokine, who handled the case of linear codes over elds. 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 p , where p is a prime. Such a code can be viewed as a submodule over the ring Z p. Because of the presence of zero-divisors in the ring, submodules do not share the useful properties of vector spaces. We get around this diiculty 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. 1 List of gure captions: 1. The trellis for a single vector (example 1) 2. The trellis from an arbitrary generator matrix (example 2) 3. The trellis for the code generated by a single vector over a ring. 4. The trellis for Example 8 5. The trellis for Example 9 6. The trellis for Example 10 7. The trellis for Example 11 8. The trellis for Example 12 2
منابع مشابه
An Efficient Algorithm for Constructing Minimal Trellises for Codes over Finite Abelian Groups
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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 compute efficiently local descriptions of the minimal trellis. This extends the work of Kschischan...
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