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2D Linear Detector Based on Generalized Belief Propagation Algorithm

Various ideas have been borrowed from 1D inter symbol interference (ISI) detectors towards approximation of near maximum likelihood (ML) detection over 2D ISI channels. Generalized belief propagation (GBP) algorithm is a graph based algorithm different from these algorithms and is observed to give the best bit error rate (BER) performance by minimizing KL-distance metric. GBP algorithm passes messages between regions instead of messages between nodes in an iterative fashion. However, GBP algorithm has a very high computational complexity and is not suitable for practical deployment. In this paper, we propose a GBP based signal detection algorithm using a quadratic approximation of the KL-distance metric. This allows us to minimize the cost function by solving a set of linear equations i.e., obtain a one shot solution instead of the iterative message passing in the GBP algorithm. We also provide an intuition into the nature of the hard decisions given by the algorithm. The idea opens up various approximations of the GBP algorithm using different convex approximations of the cost function with the desired nature of obtaining the solution. We show the efficacy of the proposed algorithm by detecting 5×5 pages of binary data over a chosen channel with 3×3 ISI span. The quadratic approximation is observed to give 1.5 dB inferior performance in signal-to-noise ratio (SNR) as compared to the GBP algorithm.