This paper presents an efficient algorithm for finding the dominant trapping sets of a low-density parity-check (LDPC) code. The algorithm can be used to estimate the error floor of LDPC codes or as a tool to design LDPC codes with low error floors. For regular codes, the algorithm is initiated with a set of short cycles as the input. For irregular codes, in addition to short cycles, variable nodes with low degree and cycles with low approximate cycle extrinsic message degree (ACE) are also used as the initial inputs. The initial inputs 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, low-degree variable nodes, and cycles with low ACE. The algorithm is universal in the sense that it can be used for an arbitrary graph and that it can be tailored to find a variety of graphical objects, such as absorbing sets and Zyablov-Pinsker 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.

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IEEE Transactions on Information Theory
Department of Systems and Computer Engineering

Karimi, M. (Mehdi), & Banihashemi, A. (2012). Efficient algorithm for finding dominant trapping sets of LDPC codes. IEEE Transactions on Information Theory, 58(11), 6942–6958. doi:10.1109/TIT.2012.2205663