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Distributed coding of correlated sources with memory poses a number of considerable challenges that threaten its practical application, particularly (but not only) in the context of sensor networks. This problem is strongly motivated by the obvious observation that most common sources exhibit temporal correlations that may be at least as important as spatial or intersource correlations. This paper presents an analysis of the underlying tradeoffs, paradigms for coding systems, and approaches for distributed predictive coder design optimization. Motivated by practical limitations on both complexity and delay (especially for dense sensor networks) the focus here is on predictive coding. From the source coding perspective, the most basic tradeoff (and difficulty) is due to conflicts that arise between distributed coding and prediction, wherein ldquostandardrdquo distributed quantization of the prediction errors, if coupled with imposition of zero decoder drift, would drastically compromise the predictor performance and hence the ability to exploit temporal correlations. Another challenge arises from instabilities in the design of closed-loop predictors, whose impact has been observed in the past, but is greatly exacerbated in the case of distributed coding. In the distributed predictive coder design, we highlight the fundamental tradeoffs encountered within a more general paradigm where decoder drift is allowable or unavoidable, and must be effectively accounted for and controlled. We derive an overall design optimization method for distributed predictive coding that avoids the pitfalls of naive distributed predictive quantization and produces an optimized low complexity and low delay coding system. The proposed iterative algorithms for distributed predictive coding subsume traditional single-source predictive coding and memoryless distributed coding as extreme special cases.