Graphs, tessellations, and perfect codes on flat tori

被引：45
作者：
Costa, SIR [1 ]
Muniz, M
Agustini, E
Palazzo, R
机构：
[1] Univ Estadual Campinas, Inst Matemat, BR-13081970 Campinas, SP, Brazil
[2] Univ Fed Parana, Ctr Politecn, BR-81531990 Curitiba, Parana, Brazil
[3] Univ Fed Uberlandia, Fac Matemat, BR-38408100 Uberlandia, MG, Brazil
[4] Univ Estadual Campinas, Dept Telemat, BR-13081970 Campinas, SP, Brazil
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2004年 / 50卷 / 10期
基金：
巴西圣保罗研究基金会;
关键词：
codes on graphs; coset codes; flat torus; geometrically uniform (GU) codes; perfect codes; spherical codes;
D O I：
10.1109/TIT.2004.834754
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Quadrature amplitude modulation (QAM)-like signal sets are considered in this paper as coset constellations placed on regular graphs on surfaces known as flat tori. Such signal sets can be related to spherical, block, and trellis codes and may be viewed as geometrically uniform (GU) in the graph metric in a sense that extends the concept introduced by Forney [13]. Homogeneous signal sets of any order can then be labeled by a cyclic group, induced by translations on the Euclidean plane. We construct classes of perfect codes on square graphs including Lee spaces, and on hexagonal and triangular graphs, all on flat tori. Extension of this approach to higher dimensions is also considered. Index Terms-Codes on graphs, coset codes, flat torus, geometrically uniform (GU) codes, perfect codes, spherical codes.
引用
收藏
页码：2363 / 2377
页数：15
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