Improved bounds on the word error probability of RA(2) codes with linear-programming-based decoding

This paper deals with the linear-programming-based decoding algorithm of Feldman and Karger for repeat-accumulate "turbo-like" codes. We present a new structural characterization that captures the event that decoding fails. Based on this structural characterization, we develop polynomial algorithms that, given an RA(2) code, compute upper and lower bounds on the word error probability P_w for the binary-symmetric and the additive white Gaussian noise (AWGN) channels. Our experiments with an implementation of these algorithms for bounding P_w demonstrate in many interesting cases an improvement in the upper bound on the word error probability by a factor of over 1000 compared to the bounds by Feldman et al.. The experiments also indicate that the improvement in upper bound increases as the codeword length increases and the channel noise decreases. The computed lower bounds on the word error probability in our experiments are roughly ten times smaller than the upper bound.