A Truncated Prediction Framework for Streaming Over Erasure Channels

Abstract

We propose a new coding technique for sequential transmission of a stream of Gauss–Markov sources over erasure channels under a zero decoding delay constraint. Our proposed scheme is a combination (hybrid) of predictive coding with truncated memory, and quantization-and-binning. We study the optimality of our proposed scheme using an information theoretic model. In our setup, the encoder observes a stream of source vectors that are spatially independent and identically distributed (i.i.d.) and temporally sampled from a first-order stationary Gauss–Markov process. The channel introduces an erasure burst of a certain maximum length $B$ , starting at an arbitrary time, not known to the transmitter. The reconstruction of each source vector at the destination must be with zero delay and satisfy a quadratic distortion constraint with an average distortion of $D$ . The decoder is not required to reconstruct those source vectors that belong to the period spanning the erasure burst and a recovery window of length $W$ following it. We study the minimum compression rate $R(B,W,D)$ in this setup. As our main result, we establish upper and lower bounds on the compression rate. The upper bound (achievability) is based on our hybrid scheme. It achieves significant gains over baseline schemes such as (leaky) predictive coding, memoryless binning, a separation-based scheme, and a group of pictures-based scheme. The lower bound is established by observing connection to a network source coding problem. The bounds simplify in the high resolution regime, where we provide explicit expressions whenever possible, and identify conditions when the proposed scheme is close to optimal. We finally discuss the interplay between the parameters of our burst erasure channel and the statistical channel models and explain how the bounds in the former model can be used to derive insights into the simulation results involving the latter. In particular, our proposed scheme outperforms the baseline schemes over the i.i.d. erasure channel and the Gilbert–Elliott channel, and achieves performance close to a lower bound in some regimes.