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A graph-based receiver is presented that iteratively performs soft channel estimation and soft data detection. Reliability information of data symbols is utilized to improve channel estimation, and in turn, soft channel estimates refine data symbol estimates. The proposed multi-dimensional factor graph introduces transfer nodes that exploit correlation of adjacent channel coefficients in an arbitrary number of dimensions (e.g. time, frequency, and spatial domain). This establishes a simple and flexible receiver structure that facilitate soft channel estimation and data detection in multi-dimensional dispersive channels, and supports arbitrary modulation and channel coding schemes. Simulation results demonstrate that the proposed multi-dimensional graph-based receiver outperforms iterative and non-iterative state-of-the-art receivers.