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The distributed video coding (DVC) paradigm constitutes a flexible framework where computational complexity can be freely distributed between encoder and decoder, hence favoring up-link oriented video applications where recording devices are modest in terms of computational power and are faced with energy consumption constraints. This contribution presents an original transform domain DVC architecture, which performs hash-based motion estimation at the decoder combined with a novel probabilistic motion compensation technique to generate side information. The proposed probabilistic motion compensation incorporates knowledge of the correlation channel statistics and extracts additional information from the hash. Experimental results report Bjontegaard rate savings of up to 4.61%, when using the novel probabilistic motion compensation method instead of our previous approach. Moreover, the compression performance of the presented DVC architecture, featuring the proposed probabilistic motion compensation, surpasses the performance of the state-of-the-art DISCOVER codec, showing Bjontegaard rate savings of up to 15.69%.