Fault-tolerant parallel linear filtering using compressive sensing

In this paper, we study the problem of designing fault-tolerant parallel linear filters. We assume that a linear filter can either function perfectly or fail completely, i.e., generate arbitrary outputs. We use real-number error correcting codes based on linear programming decoding to introduce redundancy into the linear filters and detect faulty filters. We prove that all faulty filters can be detected and corrected if the number of faulty filters is smaller than a threshold value. We also obtain simulation results to support our statement. To the best of our knowledge, we believe that this work is the first to connect the information-theoretic idea of real-number error control coding with parallel linear filtering systems.