Fast Vector Quantization Encoding Based onK-d Tree Backtracking Search Algorithm

Abstract

In this paper we consider theK-d tree-based backtracking search algorithm and study its performance in the context of vector quantization encoding of speech waveform. We discuss the basic algorithm in detail and highlight the features of optimization as observed from theoretical analysis and from the empirical performance of the backtracking search. It is seen that, despite the 2Kdependence of the theoretical average complexity bound for search inK-dimensional vector space, the actual average complexity of the backtracking search in vector quantization encoding of speech waveform is excellent. However, we show that the backtracking search has a very high worst-case computational overhead and that this may be unacceptable in many practical applications such as real-time vector quantization encoding, where the worst-case complexity is of considerable importance in addition to average computational complexity. In vector quantization applications where it is of interest to use large values ofKforr≤ 1 bit/sample, the codebook size isN≤ 2Kand the backtracking search with a performance bound of the order of 2Koffers a poor worst-case performance. We also consider the use of principal component rotation in the context of vector quantization of speech waveform where there is a high degree of correlation across the components of a vector and show that this can improve the efficiency of optimization and reduce both the main search complexity and the overhead complexity of the backtracking search.