Iterative Signal Recovery Algorithms --- A Unified View of Turbo and Message-Passing Approaches

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Over the last years, plenty of signal recovery algorithms for compressed sensing have been devised. The most effective are those based on iterative processing, specifically IHT and AMP and its variants. Basically, two different philosophies of iterative processing can be distinguished: the Turbo principle and the message passing principle. In Turbo schemes, information is passed between (typically) two blocks; the processing within each component is done jointly over each signal block (vector). Conversely, message passing utilizes a graphical model with (typically) a huge number of nodes. Information is passed between all connected nodes (elements of the vector); the processing is done locally in each node. Hence, the global view in Turbo processing compares with the local view in message passing.Even though AMP is derived from the MP view, the final algorithm can be better categorized under the Turbo principle. Very recently proposed signal recovery approaches like TSR, OAMP, VAMP, and IMS immediately follow the Turbo principle. Both worlds show striking similarities but also significant differences. A unified view of these algorithms is missing in the literature.The main objective of this proposal is to bring the Turbo and MP world closer together. The common principles and fundamental differences have to be worked out. Via a thorough analysis and categorization of the diverse variants meanwhile available, a deeper understanding shall be developed. Thereby, we are more interested in the engineering perspective rather than the large-system analysis and mathematical view; the algorithms and concepts should be reinterpreted and understood from the engineering perspective. The question of other partitionings of the problem to be solved into two subproblems over which iteration is done will be addressed. Thereby the tradeoff between performance and complexity is of particular interest. The efficiency of the different algorithms in applications from digital communications will be studied. Although analysis and synthesis will be done throughout for real-valued and discrete-valued sparse signals, stronger focus will be put on demands (e.g., no perfect recovery is required or possible) and performance measures (e.g., bit error rates) for the intended applications.