Delayed Sequential Coding of Correlated Sources

Abstract

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 ofjoint coding for all nontrivial MSE-tuples satisfying certain positive semidefiniteness conditions. Thus, even a single frame delay holds potential for yielding huge performance improvements. A ratedistortion performance equivalence of, causal sequential encoding with delayed noncausal sequential decoding, and, delayed noncausal sequential encoding with causal sequential decoding, is also established.

Tracking and Control of Gauss–Markov Processes over Packet-Drop Channels with Acknowledgments

“…-Denote the reconstruction from f t and g t−2 -namely given that b t = 1 and b t−1 = 0 -by Then, the observer sees α t Q t−1 (s t−1 ) as possible SI available at the state estimator to minimize D Weighted t as in (2). • Generates a reconstructionŝ t of the prediction errors t :…”

Achievable Moderate Deviations Asymptotics for Streaming Compression of Correlated Sources

“…However, using the condition for γ * ∈ (0, 1) given in (180), we conclude that it is impossible to satisfy (175) if γ * ∈ (0, 1). Therefore, we have proved that (25) and (26)…”

“…The proof of Proposition 3 is provided in Appendix A. Note that for any source P XY , g 1 (P XY ) ∈ R. Thus, Proposition 3, and in particular (25), allows us to conclude that for each correlated source, there exists a non-empty set of directions of approaching a boundary rate pair (R * X , R * Y ), parametrized by θ, such that we can achieve a multiplicative gain of T in the moderate deviations constant compared with Case (ii) of the nonstreaming SW coding. In addition, from Proposition 3 and the observation after (23) (namely that g 1 (P XY ) = g 2 (P XY ) ⇐⇒ V(P XY ) = V(P X|Y |P Y )), we notice that for sources P XY such that V(P XY ) = V(P X|Y |P Y ), we conclude that there will also be a non-empty set of directions of approaching the boundary in which we cannot, in general, achieve a gain of T in the streaming scenario (using the coding scheme and analyses delineated in Section V).…”

“…Matsuta and Uyematsu [24] considered the lossy source coding problem with delayed side information. Ma and Ishwar [25] focused on delayed sequential coding of correlated video sources. Zhang, Vellambi and Nguyen [26] analyzed the error exponent of lossless streaming compression of a single source using variable-length sequential random binning.…”

“…We first prove that (25) and (26) are sufficient conditions by considering the scenarios where γ * = 1 and γ * = 0. Then we prove that (25) and (26) are also necessary by considering the scenario where γ * ∈ (0, 1).…”