Vector Indexing and Lattice Vector Quantization with Reduced or without Look-up Table

This paper describes new vector indexing algorithms for Lattice Vector Quantization (LVQ). The techniques described apply to a large class of lattices such as Z n , A n , D n , D ++ n (including as special cases the Gosset Lattice E 8 , and the lattice of Barnes-wall 1 6), widely used in signal compression. Relying on a partitioning of the events sources, based on a notion of leaders, they allow to trade the vector look-up table size for arithmetic operations. A rst approach, based on a notion of 'signed' leaders, leads, at the cost of a very small number of integer arithmetic operations, to a very signiicant reduction of the vector look-up tables (also called codebooks). In a second step, the introduction of the concept of 'absolute' leaders, and of the corresponding coding and decoding algorithms, provides additional exibility in trading table size for arithmetic operations. Pursuing the goal of the best tradeoo between storage requirements and arithmetic complexity, two algorithms allowing 'on-the-y' generation of relevant portions of codebooks either of 'absolute' or of 'signed' leaders are then proposed. In addition to the interest with respect to storage requirements, these last techniques allow to avoid the problems of lattice truncating, or of vector dynamic limitations, usually encountered in LVQ. The reduction of codebook sizes leads in turn to reduced encoder and decoder complexities and allows to speed up the encoding and decoding processes. For each approach, code structures under the form of product codes with one or several components are proposed. The association of these vector indexing techniques with product codes, in the framework of Lattice Vector Quantization, leads to increased compression performances.