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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, the authors 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. They further show that adaptively adding new constraints, e.g. by combining parity checks, can provide large gains in the performance.
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