Error control systems for digital communication and storage
Error control systems for digital communication and storage
Introduction to Coding Theory
Decoding Turbo-Like Codes via Linear Programming
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Decoding error-correcting codes via linear programming
Decoding error-correcting codes via linear programming
The minimum distance of turbo-like codes
IEEE Transactions on Information Theory
The capacity of low-density parity-check codes under message-passing decoding
IEEE Transactions on Information Theory
Design of capacity-approaching irregular low-density parity-check codes
IEEE Transactions on Information Theory
Using linear programming to Decode Binary linear codes
IEEE Transactions on Information Theory
Turbo decoding as an instance of Pearl's “belief propagation” algorithm
IEEE Journal on Selected Areas in Communications
The price of privacy and the limits of LP decoding
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Message passing algorithms and improved LP decoding
Proceedings of the forty-first annual ACM symposium on Theory of computing
Spectra and minimum distances of repeat multiple-accumulate codes
IEEE Transactions on Information Theory
Linear time decoding of regular expander codes
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Linear-time decoding of regular expander codes
ACM Transactions on Computation Theory (TOCT) - Special issue on innovations in theoretical computer science 2012
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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 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 where codewords are paths through a graph. Consequently, the LP bears a strong resemblance to the rain-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 codeword.