LP decoding of regular LDPC codes in memoryless channels

We study error bounds for linear programming decoding of regular LDPC codes. For memoryless binary-input output-symmetric channels, we prove bounds on the word error probability that are inverse doubly-exponential in the girth of the factor graph. For memoryless binary-input AWGN channels, we derive lower bounds on the thresholds for regular LDPC codes under LP decoding. Specifically, we prove a lower bound of σ = 0.735 on the threshold of (3, 6)-regular LDPC codes with logarithmic girth.