Sequential Coding of Gauss-Markov Sources over Packet-Erasure Channels with Feedback

We consider the problem of sequential transmission of Gauss–Markov sources over packet-erasure channels with a possibly delayed output feedback. For the case of instantaneous feedback, we determine the optimal squared error distortions for given transmission rates for all time instants, and construct a scheme that achieves all of them simultaneously. This establishes the optimal rate–distortion region for sequential coding of Gauss– Markov sources without packet erasures, as a special case. For the case of delayed feedback, we connect the problem to that of compression with side information that is known at the encoder and may be known at the decoder — where the most recent packets serve as side information that may have been erased. We conclude the paper by demonstrating that the loss due to a delay by one time instant is rather small.

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