Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Error-correction capability of column-weight-three LDPC codes
IEEE Transactions on Information Theory
Modern Coding Theory
IEEE Transactions on Information Theory - Part 1
Good error-correcting codes based on very sparse matrices
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
Signal-space characterization of iterative decoding
IEEE Transactions on Information Theory
Expander graph arguments for message-passing algorithms
IEEE Transactions on Information Theory
Finite-length analysis of low-density parity-check codes on the binary erasure channel
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Regular and irregular progressive edge-growth tanner graphs
IEEE Transactions on Information Theory
Stopping set distribution of LDPC code ensembles
IEEE Transactions on Information Theory
Using linear programming to Decode Binary linear codes
IEEE Transactions on Information Theory
LP Decoding Corrects a Constant Fraction of Errors
IEEE Transactions on Information Theory
Asymptotic Spectra of Trapping Sets in Regular and Irregular LDPC Code Ensembles
IEEE Transactions on Information Theory
Pseudo-Codeword Analysis of Tanner Graphs From Projective and Euclidean Planes
IEEE Transactions on Information Theory
Pseudocodewords of Tanner Graphs
IEEE Transactions on Information Theory
Minimum Pseudoweight and Minimum Pseudocodewords of LDPC Codes
IEEE Transactions on Information Theory
On the Error Correction of Regular LDPC Codes Using the Flipping Algorithm
IEEE Transactions on Information Theory
An Efficient Pseudocodeword Search Algorithm for Linear Programming Decoding of LDPC Codes
IEEE Transactions on Information Theory
Probabilistic Analysis of Linear Programming Decoding
IEEE Transactions on Information Theory
Eliminating Trapping Sets in Low-Density Parity-Check Codes by Using Tanner Graph Covers
IEEE Transactions on Information Theory
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Error correction capability of column-weight-three LDPC codes under the Gallager A algorithm-Part II
IEEE Transactions on Information Theory
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We describe a family of instanton-based optimization methods developed recently for the analysis of the error floors of low-density parity-check (LDPC) codes. Instantons are the most probable configurations of the channel noise which result in decoding failures. We show that the general idea and the respective optimization technique are applicable broadly to a variety of channels, discrete or continuous, and variety of sub-optimal decoders. Specifically, we consider: iterative belief propagation (BP) decoders, Gallager type decoders, and linear programming (LP) decoders performing over the additive white Gaussian noise channel (AWGNC) and the binary symmetric channel (BSC). The instanton analysis suggests that the underlying topological structures of the most probable instanton of the same code but different channels and decoders are related to each other. Armed with this understanding of the graphical structure of the instanton and its relation to the decoding failures, we suggest a method to construct codes whose Tanner graphs are free of these structures, and thus have less significant error floors.