Error Floor Prediction of LDPC Codes
Pamela Lee, Lara Dolecek1, Zhengya Zhang, Venkat Anantharam, Martin Wainwright, Borivoje Nikolic and Sudeep Kamath
National Science Foundation CCF-0635372, Marvell, Intel, Infineon Technologies and UC MICRO
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. We develop two methods, a stochastic one based on importance sampling and a deterministic one based on high signal-to-noise ratio (SNR) asymptotics, each suitably applied to absorbing sets within the LDPC code, to predict error floors. Our results are in very close agreement with hardware-based experimental results, and moreover extend the prediction of the error probability to as low as 10-30. 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. The deterministic estimates are based on channel-independent absorbing regions and are guaranteed to be a lower bound to the error probability in the high SNR regime. The usefulness of these results is demonstrated for both the standard Gaussian channel and a channel with Gaussian mixture noise.
- L. Dolecek, Z. Zhang, M. Wainwright, V. Anantharam, and B. Nikolic, "Evaluation of the Low Frame Error Rate Performance of LDPC Codes Using Importance Sampling," IEEE Information Theory Workshop, September 2007, pp. 202-207.
- P. Lee, L. Dolecek, Z. Zhang, V. Anantharam, B. Nikolic, and M. J. Wainwright, "Error Floors in LDPC Codes: Fast Simulation, Bounds and Hardware Emulation," IEEE International Symposium on Information Theory, July 2008, pp. 444-448.
1Massachusetts Institute of Technology