  Detectability of failures of linear programming (LP) decoding and the
potential for improvement by adding new constraints motivate the use of an
adaptive approach in selecting the constraints for the underlying LP problem.
In this paper, we make a first step in studying this method, and show that it
can significantly reduce the complexity of the problem, which was originally
exponential in the maximum check-node degree. We further show that adaptively
adding new constraints, e.g. by combining parity checks, can provide large
gains in the performance.
