Zero-Delay Sequential Transmission of Markov Sources Over Burst Erasure Channels

A setup involving zero-delay sequential transmission of a vector Markov source over a burst erasure channel is studied. A sequence of source vectors is compressed in a causal fashion at the encoder, and the resulting output is transmitted over a burst erasure channel. The destination is required to reconstruct each source vector with zero-delay, but those source sequences that are observed either during the burst erasure, or in the interval of length W following the burst erasure need not be reconstructed. The minimum achievable compression rate is called the rate-recovery function. We assume that each source vector is independent identically distributed (i.i.d.) across the spatial dimension and is sampled from a stationary, first-order Markov process across the temporal dimension. For discrete sources, the case of lossless recovery is considered, and upper and lower bounds on the rate-recovery function are established. Both these bounds can be expressed as the rate for predictive coding, plus a term that decreases at least inversely with the recovery window length W. For Gauss-Markov sources and a quadratic distortion measure, upper and lower bounds on the minimum rate are established when W = 0. These bounds are shown to coincide in the high resolution limit. Finally, another setup involving i.i.d. Gaussian sources is studied and the raterecovery function is completely characterized in this case.