格及其编码和译码

Lattices and their encoding and decoding methods

本文介绍了n维实欧氏空间R^n中格的基本概念、构造与主要的编译码方法,讨论了二元纠错码与格的关系,以及由二元码构造格的方法。格与二元纠错码的软判决译码有着紧密的联系。格的最主要特点是将矢量空间R^n进行划分,在矢量量化和编码理论中具有重要的现实意义。

The basic concepts and constructions of lattices in R^n, the n-dimensional real Euclidean space, including encoding and decoding methods for lattices, are introduced. The relations between binary error-correcting codes and lattices as well as the algorithms of constructing lattices from binary codes are discussed. A close relation between lattices and soft decoding of binary error-correcting codes exists. The most important characteristic of lattices is that a lattice divides the vector space R^n, which is of important practical signifi- cance in the application of lattices to vector quanfization and coding theory.