Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
List decoding: algorithms and applications
ACM SIGACT News
Randomness conductors and constant-degree lossless expanders
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Information Theory and Reliable Communication
Information Theory and Reliable Communication
Good Codes Based on Very Sparse Matrices
Proceedings of the 5th IMA Conference on Cryptography and Coding
Linear time encodable and list decodable codes
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Decoding error-correcting codes via linear programming
Decoding error-correcting codes via linear programming
Decoding turbo-like codes via linear programming
Journal of Computer and System Sciences - Special issue on FOCS 2002
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Iterative approximate linear programming decoding of LDPC codes with linear complexity
IEEE Transactions on Information Theory
Linear-time encodable and decodable error-correcting codes
IEEE Transactions on Information Theory - Part 1
The capacity of low-density parity-check codes under message-passing decoding
IEEE Transactions on Information Theory
Efficient encoding of low-density parity-check codes
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Error exponents of expander codes
IEEE Transactions on Information Theory
On the application of LDPC codes to arbitrary discrete-memoryless channels
IEEE Transactions on Information Theory
Linear-time encodable/decodable codes with near-optimal rate
IEEE Transactions on Information Theory
Distance properties of expander codes
IEEE Transactions on Information Theory
Improved Nearly-MDS Expander Codes
IEEE Transactions on Information Theory
LP Decoding Corrects a Constant Fraction of Errors
IEEE Transactions on Information Theory
LP decoding of codes with expansion parameter above 2/3
Information Processing Letters
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Sipser and Spielman (IEEE IT, 1996) showed that any (c, d)-regular expander code with expansion parameter 3/4 is decodable in linear time from a constant fraction of errors. Feldman et al. (IEEE IT, 2007) proved that expansion parameter 2/3 + 1/3c is sufficient to correct a constant fraction of errors in polynomial time using LP decoding. In this work we give a simple combinatorial algorithm that achieves even better parameters. In particular, our algorithm runs in linear time and works for any expansion parameter 2/3−1/6c. We also prove that our decoding algorithm can be executed in logarithmic time on a linear number of parallel processors.