The Leech lattice, the octacode, and decoding algorithms (original) (raw)
1995, IEEE Transactions on Information Theory
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2017
Block codes have been wildly used in error-correcting area of information communication for many years. Recently, some researchers found that the using of lattices may reduce the bottleneck of block codes, the lattices codes may be considered for the future 5G. However, the researches on this topic are still in its infancy. In this article, we considered a different encode/decode method by using lattices theory. We first introduced and studied a lattice-valued function on a set, by which we can generate binary block codes. Moreover we discuss how to get the lattices arising from binary block codes. We introduce the notion of semigroup codes and prove that any binary semigroup code V is a lattice in the order " ≤c ". From such lattice we can construct a lattice function f which determines a binary block code V1 and (V1, ≤c) is isomorphic to (V, ≤c). For the special semigroup code V , we can get a lattice function f such that f determines a binary block code V1 and V1 = V. T...
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