A zero-delay sequential scheme for lossy coding of individual sequences

Tamás Linder and Gabor Lugosi

Economics Working Papers from Department of Economics and Business, Universitat Pompeu Fabra

Abstract: We consider adaptive sequential lossy coding of bounded individual sequences when the performance is measured by the sequentially accumulated mean squared distortion. The encoder and the decoder are connected via a noiseless channel of capacity $R$ and both are assumed to have zero delay. No probabilistic assumptions are made on how the sequence to be encoded is generated. For any bounded sequence of length $n$, the distortion redundancy is defined as the normalized cumulative distortion of the sequential scheme minus the normalized cumulative distortion of the best scalar quantizer of rate $R$ which is matched to this particular sequence. We demonstrate the existence of a zero-delay sequential scheme which uses common randomization in the encoder and the decoder such that the normalized maximum distortion redundancy converges to zero at a rate $n^{-1/5}\log n$ as the length of the encoded sequence $n$ increases without bound.

Keywords: Lossy source coding; scalar quantization; sequential prediction; individual sequences (search for similar items in EconPapers)
JEL-codes: C13 C14 (search for similar items in EconPapers)
Date: 2000-02
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