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- W2157927886 abstract "In this paper, we study the graphical structure of elementary trapping sets (ETSs) of variable-regular low-density parity-check (LDPC) codes. ETSs are known to be the main cause of error floor in LDPC coding schemes. For the set of LDPC codes with a given variable node degree dl and girth g, we identify all the nonisomorphic structures of an arbitrary class of (a, b) ETSs, where a is the number of variable nodes and b is the number of odd-degree check nodes in the induced subgraph of the ETS. This paper leads to a simple characterization of dominant classes of ETSs (those with relatively small values of a and b) based on short cycles in the Tanner graph of the code. For such classes of ETSs, we prove that any set S in the class is a layered superset (LSS) of a short cycle, where the term layered is used to indicate that there is a nested sequence of ETSs that starts from the cycle and grows, one variable node at a time, to generate S. This characterization corresponds to a simple search algorithm that starts from the short cycles of the graph and finds all the ETSs with LSS property in a guaranteed fashion. Specific results on the structure of ETSs are presented for d <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>l</sub> = 3, 4, 5, 6, g = 6, 8, and a, b ≤ 10 in this paper. The results of this paper can be used for the error floor analysis and for the design of LDPC codes with low error floors." @default.
- W2157927886 created "2016-06-24" @default.
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- W2157927886 date "2014-09-01" @default.
- W2157927886 modified "2023-10-18" @default.
- W2157927886 title "On Characterization of Elementary Trapping Sets of Variable-Regular LDPC Codes" @default.
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- W2157927886 doi "https://doi.org/10.1109/tit.2014.2334657" @default.
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