The price of privacy and the limits of LP decoding
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Message passing algorithms and improved LP decoding
Proceedings of the forty-first annual ACM symposium on Theory of computing
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
Error-correction capability of column-weight-three LDPC codes
IEEE Transactions on Information Theory
Pseudocodeword performance analysis for LDPC convolutional codes
IEEE Transactions on Information Theory
Guessing facets: polytope structure and improved LP decoder
IEEE Transactions on Information Theory
On LP decoding of nonbinary expander codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Iterative approximate linear programming decoding of LDPC codes with linear complexity
IEEE Transactions on Information Theory
LP decoding meets LP decoding: a connection between channel coding and compressed sensing
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
On trapping sets and guaranteed error correction capability of LDPC codes and GLDPC codes
IEEE Transactions on Information Theory
Error correction capability of column-weight-three LDPC codes under the Gallager A algorithm-Part II
IEEE Transactions on Information Theory
A separation algorithm for improved LP-decoding of linear block codes
IEEE Transactions on Information Theory
Dense error correction via l1-minimization
IEEE Transactions on Information Theory
The Journal of Machine Learning Research
Linear time decoding of regular expander codes
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
LP decoding of codes with expansion parameter above 2/3
Information Processing Letters
Linear-time decoding of regular expander codes
ACM Transactions on Computation Theory (TOCT) - Special issue on innovations in theoretical computer science 2012
Hi-index | 755.32 |
We show that for low-density parity-check (LDPC) codes whose Tanner graphs have sufficient expansion, the linear programming (LP) decoder of Feldman, Karger, and Wainwright can correct a constant fraction of errors. A random graph will have sufficient expansion with high probability, and recent work shows that such graphs can be constructed efficiently. A key element of our method is the use of a dual witness: a zero-valued dual solution to the decoding linear program whose existence proves decoding success. We show that as long as no more than a certain constant fraction of the bits are flipped by the channel, we can find a dual witness. This new method can be used for proving bounds on the performance of any LP decoder, even in a probabilistic setting. Our result implies that the word error rate of the LP decoder decreases exponentially in the code length under the binary-symmetric channel (BSC). This is the first such error bound for LDPC codes using an analysis based on "pseudocodewords." Recent work by Koetter and Vontobel shows that LP decoding and min-sum decoding of LDPC codes are closely related by the "graph cover" structure of their pseudocodewords; in their terminology, our result implies that that there exist families of LDPC codes where the minimum BSC pseudoweight grows linearly in the block length