Sphere-bound-achieving coset codes and multilevel coset codes

A simple sphere bound gives the best possible tradeoff between the volume p er point of an infinite array L and its error probability on an additive wh ite Gaussian noise (AWGN) channel. It is shown that the sphere bound tan be approached by a large class of coset codes or multilevel coset codes with multistage decoding, including certain binary lattices. These codes have st ructure of the kind that has been found to be useful in practice. Capacity curves and design guidance for practical codes are given. Exponential error bounds for coset codes are developed, generalizing Poltyrev's bounds for l attices. These results are based on the channel coding theorems of informat ion theory, rather than the Minkowski-Hlawka theorem of lattice theory.