Lower Bounds on the Size of Smallest Elementary and Non-Elementary Trapping Sets in Variable-Regular LDPC Codes
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Abstract
Trapping sets are known to be the main cause for the error floor of low-density parity-check (LDPC) codes. They are often classified by their size a and the number of unsatisfied check nodes b in their subgraph. Trapping sets can be partitioned into two categories of elementary and non-elementary, where the first category are those whose subgraph only contains degree-1 and degree-2 check nodes. Empirical results have shown that often the most harmful trapping sets are elementary. In this letter, we derive a lower bound on the size of the smallest non-elementary trapping sets for a given b in variable-regular LDPC codes. The derived lower bound demonstrates that the size of the smallest possible non-elementary trapping set is, in general, larger than that of an elementary trapping set with the same b value. This provides a theoretical justification as to why non-elementary trapping sets are often not among the most harmful trapping sets.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.004 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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