Title :
On limited-delay lossy coding and filtering of individual sequences
Author :
Weissman, Tsachy ; Merhav, Neri
Author_Institution :
Dept. of Electr. Eng., Technion-Israel Inst. of Technol., Haifa, Israel
Abstract :
We continue the study of adaptive schemes for the sequential lossy coding of individual sequences which was initiated by Linder and Lugosi (see IEEE Trans. Inform. Theory. (See also Proc. 2000 IEEE ISIT, Sorento, Italy, p.125, 2000). Specifically, we consider fixed-rate lossy coding systems of fixed (or zero) delay where the encoder (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 very likely to be almost as small as that of the best scheme in that set, uniformly for all individual sequences. This result can be applied to reference classes of special interest. Finally, we consider the case where the individual sequence is corrupted by noise prior to reaching the coding system, whose goal now is to reconstruct a sequence with small distortion relative to the clean individual sequence. It is shown that for the case of a finite alphabet and an invertible channel matrix, for any finite set of sliding window schemes of a given rate there exists a source code (allowed to use randomization yet adhering to the same delay constraints) which is very likely to do essentially as well as the best scheme in the class, for all individual sequences
Keywords :
adaptive codes; decoding; delays; filtering theory; random codes; rate distortion theory; sequences; set theory; source coding; telecommunication channels; adaptive sequential lossy coding; code rate; decoder; delay constraints; filtering; finite alphabet; fixed delay; fixed-rate lossy coding systems; invertible channel matrix; limited-delay lossy coding; noise; noiseless channel; randomization; rate distortion theory; sequence reconstruction; sliding window; source code; zero delay; Decoding; Delay; Distortion measurement; Filtering; Random sequences; Random variables; Rate distortion theory;
Conference_Titel :
Information Theory, 2001. Proceedings. 2001 IEEE International Symposium on
Conference_Location :
Washington, DC
Print_ISBN :
0-7803-7123-2
DOI :
10.1109/ISIT.2001.936030