An Upper Bounding Technique on the Error Floor Performance of LDPC Codes

Low-density parity-check (LDPC) codes have higher coding gains compared to algebraic codes in several configurations. However, unlike algebraic codes whose performance can be easily determined generally, the block error rate performance of an LDPC code needs to be obtained by simulations. While there are analytical methods for some structured LDPC codes that predict this performance in the low error rate regime, these provide little insight into the error floor of other (less structured) LDPC codes. In this article, we present a simple method to upper bound the error floor of LDPC codes based on a certain monotonicity assumption on the decoder. This upper bound is general enough so that under the monotonicity assumption it is valid for any error-correcting code. This upper bounding technique is useful when projecting very low block error rates (such as below 1E-14) for LDPC codes and there is no knowledge of the trapping sets.