On the Hardness of Approximating Stopping and Trapping Sets in LDPC Codes
Andrew McGregor, Olgica Milenković · 2007
We prove that approximating the size of the smallest trapping set in Tanner graphs of linear block codes, and more restrictively, LDPC codes, is NP-hard. The proof techniques rely on reductions from three NP-hard problems, the set cover, minimum three-dimensional matching, and the minimum Hamming distance problem. The ramifications of our findings are that methods used for estimating the height of the error-floor of long LDPC codes, centered around trapping set enumeration, cannot provide accurate worst-case performance predictions.