Adaptive linear programming decoding

The ability of linear programming (LP) decoding to detect failures, and its potential for improvement by the addition of new constraints, motivates the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we show that the application of such adaptive methods can significantly reduce the complexity of the LP decoding algorithm, which, in the standard formulation, is exponential in the maximum row weight of the parity-check matrix. We further show that adaptively adding new constraints, e.g. by combining parity checks, can provide large gains in LP decoder performance.