20191001
Asymptotic Average Multiplicity of Structures within Different Categories of Trapping Sets, Absorbing Sets, and Stopping Sets in Random Regular and Irregular LDPC Code Ensembles
Publication
Publication
IEEE Transactions on Information Theory , Volume 65  Issue 10 p. 6022 6043
The performance of lowdensity paritycheck (LDPC) codes in the error floor region is closely related to some substructures of the code's Tanner graph, collectively referred to as trapping sets (TSs). In this paper, we study the asymptotic average number of different types of trapping sets such as elementary TSs (ETS), leafless ETSs (LETS), absorbing sets (ABS), elementary ABSs (EABS), and stopping sets (SS), in random variableregular and irregular LDPC code ensembles. We demonstrate that, regardless of the type of the TS, as the code's length tends to infinity, the average number of a given structure tends to infinity, to a positive constant, or to zero, if the structure contains no cycle, only one cycle, or more than one cycle, respectively. For the case where the structure contains a single cycle, we derive the asymptotic expected multiplicity of the structure by counting the average number of its constituent cycles and all the possible ways that the structure can be constructed from the cycle. This, in general, involves computing the expected number of cycles of a certain length with a certain given combination of node degrees, or computing the expected number of cycles of a certain length expanded to the desired structure by the connection of trees to its nodes. The asymptotic results obtained in this work, which are independent of the block length and only depend on the code's degree distributions, are shown to be accurate even for finitelength codes.
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doi.org/10.1109/TIT.2019.2923198  
IEEE Transactions on Information Theory  
Organisation  Department of Systems and Computer Engineering 
Dehghan, A. (Ali), & Banihashemi, A. (2019). Asymptotic Average Multiplicity of Structures within Different Categories of Trapping Sets, Absorbing Sets, and Stopping Sets in Random Regular and Irregular LDPC Code Ensembles. IEEE Transactions on Information Theory, 65(10), 6022–6043. doi:10.1109/TIT.2019.2923198
