On Characterization and Efficient Exhaustive Search of Elementary Trapping Sets of Variable-Regular LDPC Codes


Recently, Karimi and Banihashemi demonstrated that a massive majority of the elementary trapping set (ETS) structures of variable-regular low-density parity-check (LDPC) codes are layered supersets (LSS) of short cycles. The LSS property corresponds to a easy search algorithm which will notice all ETSs with LSS structure starting from short cycles in a very guaranteed fashion. In this letter, we complement this characterization by demonstrating that the remaining structures of ETSs, that aren't LSS of short cycles, are all LSS of a little variety of alternative graphical structures among the Tanner graph of the code, and therefore will additionally be found efficiently. This along with the results of Karimi and Banihashemi provides a simple search algorithm that may realize all the $(a,b)$ ETSs of any variable-regular LDPC code for any size $a$ and any number of unhappy check nodes $b$ during a guaranteed fashion.

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