An efficient algorithm for finding dominant trapping sets of LDPC codes

This paper presents an efficient algorithm for finding the dominant trapping sets of a low-density parity-check (LDPC) code. This algorithm can be used to estimate the error floor of LDPC codes or to be part of the apparatus to design LDPC codes with low error floors. The algorithm is initiated with a set of short cycles as the input. The cycles are then expanded recursively to dominant trapping sets of increasing size. At the core of the algorithm lies the analysis of the graphical structure of dominant trapping sets and the relationship of such structures to short cycles. The algorithm is universal in the sense that it can be used for an arbitrary graph and that it can be tailored to find other graphical objects, such as absorbing sets and Zyablov-Pinsker (ZP) trapping sets, known to dominate the performance of LDPC codes in the error floor region over different channels and for different iterative decoding algorithms. Simulation results on several LDPC codes demonstrate the accuracy and efficiency of the proposed algorithm. In particular, the algorithm is significantly faster than the existing search algorithms for dominant trapping sets.