Explicit construction of linear sized tolerant networks
Discrete Mathematics - First Japan Conference on Graph Theory and Applications
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Information Theory and Reliable Communication
Information Theory and Reliable Communication
Decoding Turbo-Like Codes via Linear Programming
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Computationally efficient error-correcting codes and holographic proofs
Computationally efficient error-correcting codes and holographic proofs
Error Exponents of Expander Codes under Linear-Complexity Decoding
SIAM Journal on Discrete Mathematics
Efficiently decodable codes meeting Gilbert-Varshamov bound for low rates
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Decoding error-correcting codes via linear programming
Decoding error-correcting codes via linear programming
IEEE Transactions on Information Theory - Part 1
The capacity of low-density parity-check codes under message-passing decoding
IEEE Transactions on Information Theory
Expander graph arguments for message-passing algorithms
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Finite-length analysis of low-density parity-check codes on the binary erasure channel
IEEE Transactions on Information Theory
Error exponents of expander codes
IEEE Transactions on Information Theory
Using linear programming to Decode Binary linear codes
IEEE Transactions on Information Theory
Concatenated codes: serial and parallel
IEEE Transactions on Information Theory
The price of privacy and the limits of LP decoding
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Probabilistic analysis of linear programming decoding
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Instanton-based techniques for analysis and reduction of error floors of LDPC codes
IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
On LP decoding of nonbinary expander codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Hash property and fixed-rate universal coding theorems
IEEE Transactions on Information Theory
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We give a linear programming (LP) decoder that achieves the capacity (optimal rate) of a wide range of probabilistic binary communication channels. This is the first such result for LP decoding. More generally, as far as the authors are aware this is the first known polynomial-time capacity-achieving decoder with the maximum-likelihood (ML) certificate property---where output codewords come with a proof of optimality. Additionally, this result extends the capacity-achieving property of expander codes beyond the binary symmetric channel to a larger family of communication channels.Perhaps most importantly, since LP decoding performs well in practice on turbo codes and low-density parity-check (LDPC) codes (comparable to the popular "belief propagation" algorithm), this result exhibits the power of a new, widely applicable "dual witness" technique (Feldman, Malkin, Servedio, Stein and Wainwright, ISIT '04) for bounding decoder performance.For expander codes over an adversarial channel, we prove that LP decoding corrects a constant fraction of errors. To show this, we provide a new combinatorial characterization of error events that is of independent interest, and which we expect will lead to further improvements.