Locally optimal, delay-tolerant predictive source coding

While lossy predictive coding systems well-exploit statistical correlation to achieve good compression of images, video, and speech signals, the local optimality property that exists for the design of non-predictive coding systems (e.g. scalar and unconstrained vector quantization) does not hold for existing predictive coding systems. The reason is the myopic nature of the (instantaneous) predictive encoder, which performs nearest neighbor encoding of the prediction residual without considering the effect this choice has on the distortion incurred in quantizing future samples. We redress this problem in a delay-tolerant setting, proposing an iterative, locally optimal predictive encoder. For predictive quantizer design, the implication is that, unlike existing approaches, we have a locally optimal algorithm, which strictly descends in the training set distortion, and with guaranteed convergence to a locally optimal predictive quantization solution. Moreover, during operation/testing, our iterative encoding is guaranteed to yield lower distortion than standard (instantaneous) encoding, as it can iterate upon (and strictly improve upon) such encoding. A fixed delay variant of our infinite-delay system yields significant dB gains in distortion (up to 0.6 dB at 1 bit per sample) over standard DPCM encoding, in encoding first order Gauss-Markov sources with quite modest delay (a maximum encoding delay of 6 samples). Moreover, this is just the gain from our improved encoding (given a fixed quantizer/predictor) - additional gains come from our locally optimal design, over existing (suboptimal) predictive quantizer design techniques. Future work will consider extensions for higher order prediction, for predictive vector quantization, and image/video application domains.