Linear programming based detectors for two-dimensional intersymbol interference channels

Abstract

Abstract-We present and study linear programming based detectors for two-dimensional intersymbol interference channels. Interesting instances of two-dimensional intersymbol interference channels are magnetic storage, optical storage and Wyner's cellular network model.We show that the optimal maximum a posteriori detection in such channels lends itself to a natural linear programming based sub-optimal detector. We call this the Pairwise linear program detector. Our experiments show that the Pairwise linear program detector performs poorly. We then propose two methods to strengthen our detector. These detectors are based on systematically enhancing the Pairwise linear program. The first one, the Block linear program detector adds higher order potential functions in an exhaustive manner, as constraints, to the Pairwise linear program detector. We show by experiments that the Block linear program detector has performance close to the optimal detector. We then develop another detector by adaptively adding frustrated cycles to the Pairwise linear program detector. Empirically, this detector also has performance close to the optimal one and turns out to be less complex then the Block linear program detector.

Improved linear programming decoding using frustrated cycles

“…Recently, improved LP detectors based on frustrated cycles was also used in [19] for 2DISI channel. One future research direction is to investigate other combinatorial problems in graphical coding, e.g., minimum pseudocodeword weight problem, minimum Hamming distance etc.…”

Graphical Models and Belief Propagation Hierarchy for Physics-Constrained Network Flows

“…Once the loopy structure is identified one may want to modify GM, or equivalently introduce some additional constraint between beliefs associated with the loops and not linked before in the bare LP-BP. This scheme was developed in [34,35] based on the notion of frustrated cycles and an associated Constrained Satisfaction Problem (CSP) stated in terms of beliefs optimal for the original LP-BP. Similar but different heuristic approaches were also discussed in [61,62,60] for a aGM of a general position.…”

Loop calculus and bootstrap-belief propagation for perfect matchings on arbitrary graphs

“…In such cases, the LC can be used to improve upon the BP estimate for the PF (when the BP estimate is not tight) by re-summing a number of important LC terms [15,16]. As suggested in [17,18,19,20], the BP approximation to the ML problem can be improved by analyzing higher order terms of the LC (sometimes re-summing as in [20]) and using this information to modify the original GM. The hope is that when BP is run on the new GM it will be exact or, at least, improve upon its initial approximation.…”