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The Value of Frame-Delays in the Sequential Coding of Correlated Sources

The problem of sequential coding of correlated sources with causal encoding and noncausal decoding frame- delays is studied. The fundamental tradeoffs between individual frame rates, individual frame distortions, and decoding frame-delays are stated 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 sources which are spatially stationary memoryless and temporally Gauss-Markov, mean squared error (MSE) frame distortions, and a sum-rate constraint, it is shown that causal sequential encoding with one-step delayed noncausal sequential decoding exactly matches the sum-rate-MSE performance of joint coding for all nontrivial MSE-tuples satisfying certain positive semi-definiteness conditions. Generalizations to multiple frames and arbitrary frame-delays are also presented and discussed.