In this work we present a waveform speech coding system including vector quantization. This system can be seen as a vector version of the scalar ADPCM speech coder. In such system the speech samples are grouped in vectors that are coded by a vector quantizer when its prediction subtraction has been made. This prediction is obtained in the coder by a vector predictor. Due to the non-stationarity of the speech signal, the code must be continuously adapted to the local characteristics of the current input signal of the speech. We propose the use of an adaptive vector predictor that follows the speech statistics variations so the prediction error to be coded presents the minimum dynamic range. On the other side it is wellknown that the prediction error is proportional to the signal energy. To compensate this effect a vector quantizer

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