Using Geometrical Properties for Fast Indexation of Gaussian Vector Quantizers

Abstract

Vector quantization is a classical method used in mobile communications. Each sequence of d samples of the discretized vocal signal is associated to the closest d-dimensional codevector of a given set called codebook. Only the binary indices of these codevectors (the codewords) are transmitted over the channel. Since channels are generally noisy, the codewords received are often slightly different from the codewords sent. In order to minimize the distortion of the original signal due to this noisy transmission, codevectors indexed by one-bit different codewords should have a small mutual Euclidean distance. This paper is devoted to this problem of index assignment of binary codewords to the codevectors. When the vector quantizer has a Gaussian structure, we show that a fast index assignment algorithm based on simple geometrical and combinatorial considerations can improve the SNR at the receiver by 5dB with respect to a purely random assignment. We also show that in the Gaussian case this algorithm outperforms the classical combinatorial approach in the field.