Delayed Sequential Coding of Correlated Sources

Motivated by video coding applications, we study the problem of sequential coding of correlated sources with (noncausal) encoding and/or decoding frame-delays. The fundamental tradeoffs between individual frame rates, individual frame distortions, and encoding/decoding frame-delays are derived in terms of a single-letter information-theoretic characterization of the rate-distortion region for general inter-frame source correlations and certain types of (potentially frame-specific and coupled) single-letter fidelity criteria. For video sources which are spatially stationary memoryless and temporally Gauss-Markov, MSE frame distortions, and a sum-rate constraint, our results expose the optimality of differential predictive coding among all causal sequential coders. Somewhat surprisingly, causal sequential encoding with one-step delayed noncausal sequential decoding can exactly match the sum-rate-MSE performance of joint coding for all nontrivial MSE-tuples satisfying certain positive semi- deflniteness conditions. Thus, even a single frame delay holds potential for yielding huge performance improvements. A rate- distortion performance equivalence of, causal sequential encoding with delayed noncausal sequential decoding, and, delayed noncausal sequential encoding with causal sequential decoding, is also established.