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Source Coding When the Side Information May Be Delayed
For memoryless sources, delayed side information at the decoder does not
improve the rate-distortion function. However, this is not the case for more
general sources with memory, as demonstrated by a number of works focusing on
the special case of (delayed) feedforward. In this paper, a setting is studied
in which the encoder is potentially uncertain about the delay with which
measurements of the side information are acquired at the decoder. Assuming a
hidden Markov model for the sources, at first, a single-letter characterization
is given for the set-up where the side information delay is arbitrary and known
at the encoder, and the reconstruction at the destination is required to be
(near) lossless. Then, with delay equal to zero or one source symbol, a
single-letter characterization is given of the rate-distortion region for the
case where side information may be delayed or not, unbeknownst to the encoder.
The characterization is further extended to allow for additional information to
be sent when the side information is not delayed. Finally, examples for binary
and Gaussian sources are provided.Comment: revised July 201
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