Predicting error floors of structured LDPC codes: deterministic bounds and estimates

  • Authors:
  • Lara Dolecek;Pamela Lee;Zhengya Zhang;Venkat Anantharam;Borivoje Nikolic;Martin Wainwright

  • Affiliations:
  • EECS Department, Massachusetts Institute of Technology, Cambridge, MA;EECS Department, University of California, Berkeley, Berkeley, CA;EECS Department, University of California, Berkeley, Berkeley, CA;EECS Department, University of California, Berkeley, Berkeley, CA;EECS Department, University of California, Berkeley, Berkeley, CA;EECS Department, University of California, Berkeley, Berkeley, CA

  • Venue:
  • IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
  • Year:
  • 2009

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Abstract

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.