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 ...
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.
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