LDPC Code Density Evolution in the Error Floor Region

This short paper explores density evolution (DE) for low-density parity-check (LDPC) codes at signal-to-noise-ratios (SNRs) that are significantly above the decoding threshold. The focus is on the additive white Gaussian noise channel and LDPC codes in which the variable nodes have regular degree. Prior work, using DE, produced results in the error floor region which were asymptotic in the belief-propagation decoder's log-likelihood ratio (LLR) values. We develop expressions which closely approximate the LLR growth behavior at moderate LLR magnitudes. We then produce bounds on the mean extrinsic check-node LLR values required, as a function of SNR, such that the growth rate of the LLRs exceeds that of a particular trapping set's internal LLRs such that its error floor contribution may be eliminated. We find that our predictions for the mean LLRs to be accurate in the error floor region, but the predictions for the LLR variance to be lacking beyond several initial iterations.