Causal transform coding, generalized MIMO linear prediction, and application to vectorial DPCM coding of multichannel audio

The optimal causal (prediction based) decorrelating scheme is applied to the frameworks of transform coding, coding of vectorial signals (multichannel audio), and vectorial DPCM coding. We analyze the effects of backward adaptation upon the prediction operations and compare the expressions of the coding gains under infinite and high resolution assumption. We generalize the MIMO (multiple input/multiple output) prediction by organizing differently the samples in the vectorial signals, which correspond to different degrees of non-causality of the intersignal predictors. An extreme case is the triangular MIMO prediction, for which "causality" becomes processing the channel in a certain order. The high resolution coding gain suggests an optimal strategy in the choice of the interband predictors. For two-dimensional vectorial sources (such as stereo signals) we show the superiority in terms of coding gain of the triangular MIMO predictor over classical MIMO prediction. A theorem is established which concerns the optimal ordering of the signals for the triangular MIMO predictor. When finite prediction orders are used to perform the intersignal decorrelation, we show that the optimal positioning of a finite number of taps is fairly straightforward