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Moderate-density parity-check codes from projective bundles.
- Source :
- Designs, Codes & Cryptography; Dec2022, Vol. 90 Issue 12, p2943-2966, 24p
- Publication Year :
- 2022
-
Abstract
- New constructions for moderate-density parity-check (MDPC) codes using finite geometry are proposed. We design a parity-check matrix for the main family of binary codes as the concatenation of two matrices: the incidence matrix between points and lines of the Desarguesian projective plane and the incidence matrix between points and ovals of a projective bundle. A projective bundle is a special collection of ovals which pairwise meet in a unique point. We determine the minimum distance and the dimension of these codes, and we show that they have a natural quasi-cyclic structure. We consider alternative constructions based on an incidence matrix of a Desarguesian projective plane and compare their error-correction performance with regards to a modification of Gallager's bit-flipping decoding algorithm. In this setting, our codes have the best possible error-correction performance after one round of bit-flipping decoding given the parameters of the code's parity-check matrix. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09251022
- Volume :
- 90
- Issue :
- 12
- Database :
- Complementary Index
- Journal :
- Designs, Codes & Cryptography
- Publication Type :
- Academic Journal
- Accession number :
- 160180506
- Full Text :
- https://doi.org/10.1007/s10623-022-01054-y