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
Probabilistic analysis of linear programming decoding
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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
A cutting-plane method based on redundant rows for improving fractional distance
IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
Toward optimizing Cauchy matrix for Cauchy Reed-Solomon code
IEEE Communications Letters
Improved random redundant iterative HDPC decoding
IEEE Transactions on Communications
Distributed in-network channel decoding
IEEE Transactions on Signal Processing
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
IEEE Transactions on Information Theory
Guessing facets: polytope structure and improved LP decoder
IEEE Transactions on Information Theory
Linear-programming decoding of nonbinary linear codes
IEEE Transactions on Information Theory
On Linear Programming Decoding on a Quantized Additive White Gaussian Noise Channel
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Valid inequalities for binary linear codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Variable length lossy coding using an LDPC code
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Multi-stage decoding of LDPC codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Absdet-pseudo-codewords and perm-pseudo-codewords: definitions and properties
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Analysis of error floors of LDPC codes under LP decoding over the BSC
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
On LP decoding of nonbinary expander codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
An LP decoding algorithm based on primal path-following interior point method
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Coding theorem for general stationary memoryless channel based on hash property
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
Minimum distance and pseudodistance lower bounds for generalised LDPC codes
International Journal of Information and Coding 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
LDPC decoding strategies for two-dimensional magnetic recording
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Improving the performance of LP decoders for cyclic codes
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
On trapping sets and guaranteed error correction capability of LDPC codes and GLDPC codes
IEEE Transactions on Information Theory
Analysis of absorbing sets and fully absorbing sets of array-based LDPC codes
IEEE Transactions on Information Theory
Hash property and coding theorems for sparse matrices and maximum-likelihood coding
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
Hash property and fixed-rate universal coding theorems
IEEE Transactions on Information Theory
A separation algorithm for improved LP-decoding of linear block codes
IEEE Transactions on Information Theory
Low power logic for statistical inference
Proceedings of the 16th ACM/IEEE international symposium on Low power electronics and design
Interior point decoding for linear vector channels based on convex optimization
IEEE Transactions on Information Theory
Lossy source compression using low-density generator matrix codes: analysis and algorithms
IEEE Transactions on Information Theory
On the decomposition method for linear programming decoding of LDPC codes
IEEE Transactions on Communications
On iterative compressed sensing reconstruction of sparse non-negative vectors
Proceedings of the 4th International Symposium on Applied Sciences in Biomedical and Communication Technologies
Stopping set distributions of algebraic geometry codes from elliptic curves
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
LP decoding of codes with expansion parameter above 2/3
Information Processing Letters
Constructing rate 1/p systematic binary quasi-cyclic codes based on the matroid theory
Designs, Codes and Cryptography
Hi-index | 755.68 |
A new method is given for performing approximate maximum-likelihood (ML) decoding of an arbitrary binary linear code based on observations received from any discrete memoryless symmetric channel. The decoding algorithm is based on a linear programming (LP) relaxation that is defined by a factor graph or parity-check representation of the code. The resulting "LP decoder" generalizes our previous work on turbo-like codes. A precise combinatorial characterization of when the LP decoder succeeds is provided, based on pseudocodewords associated with the factor graph. Our definition of a pseudocodeword unifies other such notions known for iterative algorithms, including "stopping sets," "irreducible closed walks," "trellis cycles," "deviation sets," and "graph covers." The fractional distance dfrac of a code is introduced, which is a lower bound on the classical distance. It is shown that the efficient LP decoder will correct up to ┌dfrac/2┐-1 errors and that there are codes with dfrac=Ω(n1-ε). An efficient algorithm to compute the fractional distance is presented. Experimental evidence shows a similar performance on low-density parity-check (LDPC) codes between LP decoding and the min-sum and sum-product algorithms. Methods for tightening the LP relaxation to improve performance are also provided.