Rate distortion efficiency of subband coding with crossband prediction

Traditional subband coding, where each subband is encoded independently, has been shown by Fischer (1992) to be suboptimum for encoding Gaussian sources in the rate-distortion sense. We show here that if we use prediction across subbands when encoding Gaussian sources, the resulting coder is asymptotically rate-distortion-optimum at high rate. We also show for Gauss-Markov sources that although the crossband prediction filter in this case is of infinite impulse response, the filter can be implemented very efficiently to high accuracy due to the fast decay of the filter coefficients.