An efficient algorithm for constructing minimal trellises for codes over finite Abelian groups
An efficient algorithm for constructing minimal trellises for codes over finite Abelian groups
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一种为有限阿贝尔群上的码构造最小网格的有效算法
DOI：
10.1109/sfcs.1996.548473
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
B. S. Rajan
中科院分区：
文献类型：
--
作者：
V. Vazirani;H. Saran;B. S. Rajan
给出了有限阿贝尔群上群码的生成矩阵，给出了计算群码的最小网格的一个有效算法。我们还展示了如何计算这样的代码的最小网格的简洁表示，并提出算法，使用这些信息来有效地计算本地的最小网格的描述。这扩展了Kschischang和Sorokine（1995）的工作，他们处理了域上线性码的情况。我们的算法的一个重要应用是最小格的建设。在我们的工作中的一个关键步骤是处理循环群C/sub p//spl alpha/上的码，其中p是素数。这样的码可以看作环Z/sub p//spl alpha/上的子模。由于环中零因子的存在，子模不具有向量空间的有用性质。我们通过将线性组合的概念限制为p-线性组合，并引入p-生成序列的概念来解决这个困难，p-生成序列具有与向量空间的生成矩阵类似的性质。
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.
影响因子：
2.5
作者：
UNGERBOECK, G
通讯作者：
UNGERBOECK, G