On Delayed Sequential Coding of Correlated Sources

Motivated by video coding applications, the problem of sequential coding of correlated sources with encoding and/or decoding frame-delays is studied. 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. The sum-rate-distortion region is characterized in terms of generalized directed information measures highlighting their role in delayed sequential source coding problems. 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 idealized differential predictive coding among all causal sequential coders, when the encoder uses a positive rate to describe each frame. Somewhat surprisingly, causal sequential encoding with one-frame-delayed noncausal sequential decoding can exactly match the sum-rate-MSE performance of joint coding for all nontrivial MSE-tuples satisfying certain positive semi-definiteness conditions. Thus, even a single frame-delay holds potential for yielding significant performance improvements. Generalizations to higher order Markov sources are also presented and discussed. A rate-distortion performance equivalence between, causal sequential encoding with delayed noncausal sequential decoding, and, delayed noncausal sequential encoding with causal sequential decoding, is also established.