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Accurate subband coding with low resolution quantization

Redundant signal expansions exhibit robustness to degradation by additive noise, at a degree which is proportional to expansion redundancy. This property can be exploited for obtaining accurate signal representations with low resolution quantization, and it has been used in oversampled A/D conversion. A problem with this approach to source coding is that the bit-rate increases linearly with expansion redundancy giving poor rate-distortion performances. Entropy coding schemes that could remedy the problem of fast increase of the bit-rate have not yet been studied in general. An example of a redundant expansion which is amenable to efficient encoding of quantized samples is discussed. A quantitative characterization of noise reduction properties of redundant expansions is given first. Then, a subband coding scheme based on overcomplete short-time Fourier expansions and low resolution quantization is discussed. This scheme allows for efficient lossless encoding of quantized expansion coefficients, with a logarithmic increase of the bit-rate with redundancy. Thus, it attains an exponential error decay in the bit-rate.