Lattices and their encoding and decoding methods
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.