Lattice codebook enumeration for generalized Gaussian source

Abstract

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/sub p/-norms in the range 0<p/spl les/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/sup n/ lattice, can be generalized to other lattices like the D/sub n/.