On the Wyner-Ziv Source Coding Problem with Unknown Delay

Tetsunao MATSUTA  Tomohiko UYEMATSU  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E97-A   No.12   pp.2288-2299
Publication Date: 2014/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E97.A.2288
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Shannon Theory
delay,  rate-distortion function,  side information,  source coding,  

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In this paper, we consider the lossy source coding problem with delayed side information at the decoder. We assume that delay is unknown but the maximum of delay is known to the encoder and the decoder, where we allow the maximum of delay to change with the block length. In this coding problem, we show an upper bound and a lower bound of the rate-distortion (RD) function, where the RD function is the infimum of rates of codes in which the distortion between the source sequence and the reproduction sequence satisfies a certain distortion level. We also clarify that the upper bound coincides with the lower bound when maximums of delay per block length converge to a constant. Then, we give a necessary and sufficient condition in which the RD function is equal to that for the case without delay. Furthermore, we give an example of a source which does not satisfy this necessary and sufficient condition.