In this paper, we propose a characterization of elementary trapping sets (ETSs) for irregular low-density parity-check (LDPC) codes. These sets are known to be the main culprits in the error floor region of such codes. The proposed characterization is based on a hierarchical graphical representation of ETSs, starting from simple cycles of the graph, or from single variable nodes, and involves three simple expansion techniques: depth-one tree (dot), path and lollipop, thus, the terminology dpi characterization. The proposed dpl characterization corresponds to an efficient search algorithm, that, for a given irregular LDPC code, can find all the instances of (a, b) ETSs with size a and with the number of unsatisfied check nodes b, within any range of interest a ≤ amax and b ≤ bmax, exhaustively. Simulation results are presented to show the versatility of the search algorithm, and to demonstrate that, compared to the literature, significant improvement in search speed can be obtained.
2017 IEEE International Symposium on Information Theory, ISIT 2017
Department of Systems and Computer Engineering

Hashemi, Y. (Yoones), & Banihashemi, A. (2017). Characterization and efficient exhaustive search algorithm for elementary trapping sets of irregular LDPC codes. In IEEE International Symposium on Information Theory - Proceedings (pp. 1192–1196). doi:10.1109/ISIT.2017.8006717