Sampling algorithms for lattice Gaussian codes

We consider the problem of sampling a discrete Gaussian distribution whose support is an n-dimensional lattice. Fast sampling algorithms for lattices decomposed as a finite union of cosets are proposed. This includes the low dimensional lattices with the best coding gains, their duals, and the 24 dimensional Leech lattice. Our methods are then applied to assess the performance of recent sampling-based codes for the AWGN channel, illustrating the gains of the discrete Gaussian distribution. In the derivation of our algorithms, a number of results concerning the theta series of notable lattices will be discussed, including relations between the theta series and its derivatives to the power and rate of a lattice Gaussian code.