On the Hardness of Approximating Stopping and Trapping Sets

We prove that approximating the size of stopping and trapping sets in Tanner graphs of linear block codes, and more restrictively, the class of low-density parity-check (LDPC) codes, is NP-hard. The ramifications of our findings are that methods used for estimating the height of the error-floor of moderate- and long-length LDPC codes, based on stopping and trapping set enumeration, cannot provide accurate worst-case performance predictions for most codes.