A Fast Index Assignment Algorithm for Vector Quantization over Noisy Transmission Channels

Vector quantisation, a widely used technique in low-bit rate coding of speech signals, is highly sensitive to errors in the transmitted codeword caused by noise in the transmission channel. This paper describes an e cient index assignment algorithm, based on Hall's solution to the quadratic assignment problem, used to re-order the codebook such that the e ect of transmission errors is minimised. Introduction Given p dimensional unlabelled data Y = fy1;y2; : : : ;ymg IR p representative of a data manifold V IR, the process of vector quantisation [1] attempts to partition V into a number of sub-regions Vi using a nite set of reference or code book vectors, W = fw1;w2;w3; : : : ;wng. The values of the reference vectors are chosen so as to minimise the quantisation error, measured according to a distance metric, between a training vector yi and the best matching reference vector w(yi) over all vectors in Y . An input vector v 2 Vi is mapped onto the most similar reference vector wi. The incoming vector can then be represented by the index i.