Multistage integer-to-integer multichannel prediction for scalable lossless coding

We present a lossless coding procedure based on a recently introduced decorrelating scheme, where both intra- and interchannel redundancies are removed by lossless prediction. The resulting signals are scalar entropy coded. We show that for continuous-amplitude Gaussian sources discretized with uniform scalar quantizers, no suboptimality occurs in the proposed lossless coding scheme by using scalar instead of vector entropy coders, except from a term caused by the lossless constraint, which vanishes in the limit of small distortions. This lossless constraint is described in terms of excess bit rate. The proposed coder may be used either as a compressor, or as a scalable lossless coder. In this case, a multistage version of the lossless coder based on ADPCM-like lossless prediction loops allows one to transmit the data by means of substreams, which represent different resolution levels. We show that this multiresolution approach is slightly suboptimal in comparison with a single global compression because of the noise feedback created in the ADPCM-like loops, but not of the space filling loss of the scalar quantizers. We propose a strategy to fix the stepsizes of these quantizers so that the delivered rates approach some predetermined target rates.