On limited-delay lossy coding and filtering of individual sequences

Abstract--We continue the study of adaptive schemes for the sequential lossy coding of individual sequences which was recently initiated by Linder and Lugosi. Specifically, we consider fixed-rate lossy coding systems of fixed (or zero) delay where the encoder (which is allowed to use randomization) and the decoder are connected via a noiseless channel of a given capacity. It is shown that for any finite set of such coding schemes of a given rate, there exists a source code (adhering to the same structural and delay limitations) with the same rate whose distortion is with high probability almost as small as that of the best scheme in that set, uniformly for all individual sequences. Applications of this result to reference classes of special interest are outlined. These include the class of scalar quantizers, trellis encoders with sliding block decoders, and differential pulse code modulator (DPCM)-based source codes. In particular, for the class of all scalar quantizers, a source code ...

• Type: Journal
• Year: 2002
• Where: TIT
• Authors: Tsachy Weissman, Neri Merhav
• Keywords: Individual Sequences, Lossy Coding, Source Code, TIT 2002