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This paper considers real time joint source-channel coding of a Markov source over a discrete memoryless channel with noiseless feedback. The encoder incurs a cost which is minimized along with a real-time end-to-end distortion. The problem is mapped to a partially observable Markov decision problem and the corresponding optimality equations, in the form of dynamic programming equations, are derived. As a consequence of the dynamic programming formulation, basic structural properties of the optimal encoding and decoding strategies are established. In addition, the problem formulation and solution obtained for dynamic joint source-channel coding with noiseless feedback is shown to encompass a much broader class of problems including that of information acquisition and real time tracking.