Error Correction Capability of LP Decoding

Introduction
There are two ways to estimate the capacity of the LP decoding, from the dual problem point of view and for the primal problem point of view. The first threshold of LP decoding was proposed by Feldman. It was analyzed in the dual domain. A dual-feasible point, dual witness, was proposed, and by the expander arguments, it can be shown that the dual witness exists. In 2009, the optimality of the primal solution was investigated by Arora, Daskalakis and Steurer. An local optimality condition for a codeword was proposed. They showed that if the codeword is locally optimal, it is globally optimal as well.