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We study error bounds for linear programming decoding of regular LDPC codes.For memoryless binary-input output-symmetric channels, we prove bounds on theword error probability that are inverse doubly-exponential in the girth of thefactor graph. For memoryless binary-input AWGN channel, we prove lower boundson the threshold for regular LDPC codes whose factor graphs have logarithmicgirth under LP-decoding. Specifically, we prove a lower bound of $\sigma=0.735$(upper bound of $\frac{Eb}{N_0}=2.67$dB) on the threshold of $(3,6)$-regularLDPC codes whose factor graphs have logarithmic girth.  Our proof is an extension of a recent paper of Arora, Daskalakis, and Steurer[STOC 2009] who presented a novel probabilistic analysis of LP decoding over abinary symmetric channel. Their analysis is based on the primal LPrepresentation and has an explicit connection to message passing algorithms. Weextend this analysis to any MBIOS channel.

LP Decoding of Regular LDPC Codes in Memoryless Channels