Lattice codebook enumeration for generalized Gaussian source

The goal of this correspondence is to propose a low-complexity enumeration algorithm for lattice vectors, based on a geometrical interpretation and valid for different source distributions, i.e., for different L-p-norms in the range 0 p less than or equal to 2. As a particular case, we obtain the Laplacian enumeration formula of Fischer. This point of view offers various advantages and particularly it enables one to make the link with the generalized theta-series and to reduce the algorithm to the calculation of a few convolutional products in the special cases p = 1 and p = 2. Using a dedicated digital signal processing (DSP) architecture, convolutional products are easy to implement and require few arithmetic operations. Our algorithm, developed for the Z(n) lattice, can be generalized to other lattices like the D-n.