Small stopping sets in projective low-density parity-check codes
| Autor: | Yu Tsunoda, Yuichiro Fujiwara |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Discrete mathematics
060102 archaeology 020206 networking & telecommunications Data_CODINGANDINFORMATIONTHEORY 06 humanities and the arts 02 engineering and technology Upper and lower bounds Set (abstract data type) Matrix (mathematics) 0202 electrical engineering electronic engineering information engineering Erasure 0601 history and archaeology Projective plane Low-density parity-check code Decoding methods Computer Science::Information Theory Mathematics Incidence (geometry) |
| Zdroj: | ITW |
| Popis: | It is known that redundant parity-check equations can improve the performance of an LDPC code by reducing the number of harmful substructures in the parity-check matrix. However, it is a difficult problem to design a parity-check matrix in such a way that it avoids substructures that are known to be harmful to iterative decoding while keeping the number of redundant parity-check equations moderate and ensuring other desirable properties. We explicitly give redundant parity-check matrices for cyclic regular LDPC codes of length n and minimum distance $d \sim \sqrt{n}$ in which there are only n parity-check equations but no stopping sets of size d+1 or smaller except for those that correspond to the nonzero codewords of the smallest weight. We do this by showing that the well-known projective LDPC codes from the incidence matrices of projective planes PG(2, q) with q even have this property. This result may give insight into how the small number of redundant parity-check equations in the geometric LDPC codes may be contributing to the good performance reported in the literature. We also give a slightly improved upper bound on the size of a smallest generic erasure correcting set. |
| Databáze: | OpenAIRE |
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