Vectorial DPCM coding and application to wideband speech coding

This paper deals with optimal coding for vectorial signals by means of a decorrelating transform such as DPCM. We show that the optimal causal transform corresponds to a (lower-diagonal-upper) triangular factorization of the autocorrelation matrix of the signal : the transformation matrix is triangular and unit diagonal. Each one of its rows is the optimal prediction filter for the corresponding component of the vector to be coded. We analyze the effect on the coding gain of the perturbation due to backward adaptation (prediction based on the quantized signal), as for DPCM coders. We then show that two previously introduced transformations, in the context of subband coding, appear as special cases of vectorial DPCM coding, and we compare these two transformations when perturbations occur on the reference signal. Finally, we apply some results of vectorial DPCM coding to wideband speech coding