Decoding turbo-like codes via linear programming
Journal of Computer and System Sciences - Special issue on FOCS 2002
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
IEEE Transactions on Information Theory
Operations Research Letters
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We introduce a novel algorithm for decoding turbo-like codes based on linear programming. We prove that for the case of Repeat-Accumulate (RA) codes, under the binary symmetric channel with a certain constant threshold bound on the noise, the error probability of our algorithm is bounded by an inverse polynomial in the code length.Our linear program (LP) minimizes the distance between the received bits and binary variables representing the code bits. Our LP is based on a representation of the code wherecode words are paths through a graph. Consequently, the LP bears a strong resemblance to the min-cost flow LP. The error bounds are based on an analysis of the probability, over the random noise of the channel, that the optimum solution to the LP is the path corresponding to the original transmitted code word.