On the hardness of approximating stopping and trapping sets

Authors:
Andrew McGregor;Olgica Milenkovic
Affiliations:
Department of Computer Science, University of Massachusetts, Amherst, MA;Department of Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, IL
Venue:
IEEE Transactions on Information Theory
Year:
2010

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Abstract

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 accurateworst-case performance predictions for most codes.