Rate distortion theory and predictive coding

In previous papers on digital coding we have stressed the importance of taking proper account of the masking properties of the human ear in order to minimize the subjective loudness of the quantizing noise. The resulting optimal quantizing noise spectrum is in general not flat and requires the use of noise-shaping filters. This masking of the quantizing noise by the speech signal itself has allowed us to use very low bit rates (less than 1 bit/sample for the prediction residual in aa adaptive predictive coder) while maintaining high speech quality. However, if the low bit rates are realized by a (coarse) instantaneous qnantizer, the quantizing error is not white and the noise-shaping filter (in the feedback loop around the quantizer) does not produce the intended noise spectrum. In this paper, we therefore describe non-instantaneous, tree-coding methods that allow the attainment of even lower bit rates (near the theoretical rate-distortion limit) with the precise optimum noise spectrum.