Vector Predictive Coding of Speech at 16 kbits/s

Abstract

Vector quantization, in its simplest form, may be regarded as a generalization of PCM (independent quantization of each sample of a waveform) to what might be called "vector PCM," where a block of consecutive samples, a vector, is simultaneously quantized as one unit. In theory, a performance arbitrarily close to the ultimate rate-distortion limit is achievable with waveform vector quantization if the dimension of the vector, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> , is large enough. The main obstacle in effectively using vector quantization is complexity. A vector quantizer of dimension <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> operating at a rate of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</tex> bits/sample requires a number of computations on the order of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k2^{kr}</tex> and a memory of the same order. However, a low-dimensional vector quantizer (dimensions 4-8) achieves a remarkable improvement over scalar quantization (PCM). Consequently, using the vector quantizer as a building block and imbedding it with other waveform data compression techniques may lead to the development of a new and powerful class of waveform coding systems. This paper proposes and analyzes a waveform coding system, adaptive vector predictive coding (AVPC), in which a low-dimensionality vector quantizer is used in an adaptive predictive coding scheme. In the encoding process, a locally generated prediction of the current input vector is subtracted from the current vector, and the resulting error vector is coded by a vector quantizer. Each frame consisting of many vectors is classified into one of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</tex> statistical types. This classification determines which one of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</tex> fixed predictors and of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</tex> vector quantizers will be used for encoding the current frame.