The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The capacity of low-density parity-check codes under message-passing decoding
IEEE Transactions on Information Theory
Signal-space characterization of iterative decoding
IEEE Transactions on Information Theory
Finite-length analysis of low-density parity-check codes on the binary erasure channel
IEEE Transactions on Information Theory
Extrinsic information transfer functions: model and erasure channel properties
IEEE Transactions on Information Theory
Regular and irregular progressive edge-growth tanner graphs
IEEE Transactions on Information Theory
Improved Probabilistic Bounds on Stopping Redundancy
IEEE Transactions on Information Theory
Eliminating Trapping Sets in Low-Density Parity-Check Codes by Using Tanner Graph Covers
IEEE Transactions on Information Theory
Average Stopping Set Weight Distributions of Redundant Random Ensembles
IEEE Transactions on Information Theory
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High error floors in optimized irregular LDPC codes limit their usage in applications that require low error rates. We introduce new methods for lowering the error floor of LDPC codes, based on enhancing the code's parity-check matrix with additional linearly dependent and independent parity-checks. We prove NP hardness of certain optimization problems related to proposed methods and provide upper bound on the number of parity-checks that need to be added. We show that the proposed methods can lower the error floor of the code significantly, by several orders of magnitude, at negligible or no rate penalty.