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We present and study linear programming based detectors for two-dimensionalintersymbol interference channels. Interesting instances of two-dimensionalintersymbol interference channels are magnetic storage, optical storage andWyner's cellular network model.  We show that the optimal maximum a posteriori detection in such channelslends itself to a natural linear programming based sub-optimal detector. Wecall this the Pairwise linear program detector. Our experiments show that thePairwise linear program detector performs poorly. We then propose two methodsto strengthen our detector. These detectors are based on systematicallyenhancing the Pairwise linear program. The first one, the Block linear programdetector adds higher order potential functions in an {\em exhaustive} manner,as constraints, to the Pairwise linear program detector. We show by experimentsthat the Block linear program detector has performance close to the optimaldetector. We then develop another detector by  {\em adaptively} adding frustrated cycles to the Pairwise linear programdetector. Empirically, this detector also has performance close to the optimalone and turns out to be less complex then the Block linear program detector.

Linear Programming based Detectors for Two-Dimensional Intersymbol Interference Channels