Modern Coding Theory
Analysis of absorbing sets and fully absorbing sets of array-based LDPC codes
IEEE Transactions on Information Theory
Introduction to Rare Event Simulation
Introduction to Rare Event Simulation
Optimization of LDPC-coded turbo CDMA systems
IEEE Transactions on Signal Processing
An adaptive spatial diversity receiver for non-Gaussianinterference and noise
IEEE Transactions on Signal Processing
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
Improved low-density parity-check codes using irregular graphs
IEEE Transactions on Information Theory
The capacity of low-density parity-check codes under message-passing decoding
IEEE Transactions on Information Theory
Importance sampling for tanner trees
IEEE Transactions on Information Theory
Analysis of absorbing sets and fully absorbing sets of array-based LDPC codes
IEEE Transactions on Information Theory
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Constructing short-length irregular LDPC codes with low error floor
IEEE Transactions on Communications
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The error-correcting performance of low-density parity check (LDPC) codes, when decoded using practical iterative decoding algorithms, is known to be close to Shannon limits for codes with suitably large blocklengths. A substantial limitation to the use of finite-length LDPC codes is the presence of an error floor in the low frame error rate (FER) region. This paper develops a deterministic method of predicting error floors, based on high signal-to-noise ratio (SNR) asymptotics, applied to absorbing sets within structured LDPC codes. The approach is illustrated using a class of array-based LDPC codes, taken as exemplars of high-performance structured LDPC codes. The results are in very good agreement with a stochastic method based on importance sampling which, in turn, matches the hardware-based experimental results. The importance sampling scheme uses a mean-shifted version of the original Gaussian density, appropriately centered between a codeword and a dominant absorbing set, to produce an unbiased estimator of the FER with substantial computational savings over a standard Monte Carlo estimator. Our deterministic estimates are guaranteed to be a lower bound to the error probability in the high SNR regime, and extend the prediction of the error probability to as low as 10-30. By adopting a channel-independent viewpoint, the usefulness of these results is demonstrated for both the standard Gaussian channel and a channel with mixture noise.