This paper describes vector indexing algorithms valid for a large class of lattices (Z/sub n/, A/sub n/, D/sub n/, and D/sub n//sup ++/ including as special cases the Gosset (E/sub 8/) and Barnes-Wall (/spl Lambda//sub 16//sup n/) lattices), widely used in audio-visual signal compression. The indexing mechanism relies on reverse lexicographic ordering of the vectors, in classes of equivalence defined as sets of vectors obtained by "signed" permutations of the components of initial vectors called leaders. The approach makes it possible to trade the size of the lookup tables-or codebooks-for arithmetic operations. The reduction of codebook sizes leads in turn to reduced encoder and decoder complexities. Pursuing the goal of best tradeoff between storage requirements and arithmetic complexity, two algorithms, based on the proposed indexing mechanisms, allowing "on-the-fly" generation of adaptive portions of codebooks are then described. These algorithms make it possible to overcome the problems of lattice truncating usually encountered in lattice vector quantization (LVQ). Combined with product codes, these indexing techniques lead to increased compression performances.

Rate-distortion optimization procedures are very often used in rate allocation problems encountered in source encoders. However, these procedures can be, depending on the number of quantizers considered, very time consuming. This paper describes a simplified approach relying on statistical signal and noise modeling. The strategy presented leads to performances comparable to a classical rate-distortion procedure with a significant reduction of computational cost, making real-time implementations very feasible.