Streaming of Markov Sources over Burst Erasure Channels

Real-time streaming communication systems require both the sequential encoding of information sources and playback under strict latency constraints. The central focus of this thesis is on the fundamental limits of such communication systems in the presence of packet losses. In practice packet losses are unavoidable due to fading in wireless channels or congestion in wired networks. While several ad hoc approaches are used to deal with packet losses in streaming systems, in this thesis we examine these approaches using an information theoretic framework.In our setup, the source process is a sequence of vectors sampled from a spatially i.i.d. and temporally a first-order stationary Markov distribution. The encoder sequentially compresses these source vectors into channel packets. The channel may introduce a burst erasure of length up to B in an unknown location during the transmission period, and perfectly reveals the rest of the packets to the destination. The decoder is interested in reconstructing the source vectors with zero delay, except those at the time of erasure and a window of length W following it. The minimum attainable compression rate for this setup R(B,W), termed the rate-recovery function, is investigated for discrete source with lossless recovery, and Gauss-Markov sources with a quadratic distortion measure. The above setup introduces a new problem in network information theory. Our key contributions include: (1) Upper and lower bounds on the rate-recovery function for discrete memoryless sources and lossless recovery, which coincide in some special cases. (2) A new coding scheme for the Gauss-Markov sources and a quadratic distortion measure. This scheme can be interpreted as a hybrid between predictive coding and memoryless quantization-and-binning. (3) Extensions of our zero-delay setup to incorporate non-zero decoding delays. We further show that our proposed hybrid coding scheme yields significant performance gains over baseline schemes such as predictive coding, memoryless quantization-and-binning and interleaving, over statistical channels such as the i.i.d. erasure channel and the Gilbert Elliott channel, and performs close to optimally, over a wide range of channel parameters. While our information theoretic framework involves coding theorems for burst-erasure channels our resulting schemes are applicable for much broader class of erasure channels and can yield significant performance gains in practice.

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