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On the Decoding of Lattices Constructed via a Single Parity Check.
- Source :
- IEEE Transactions on Information Theory; May2022, Vol. 68 Issue 5, p2951-2968, 18p
- Publication Year :
- 2022
-
Abstract
- This paper investigates the decoding of a remarkable set of lattices: We treat in a unified framework the Leech lattice in dimension 24, the Nebe lattice in dimension 72, and the Barnes-Wall lattices. A new interesting lattice, named $L_{3\cdot 24}$ , is constructed as a simple application of the single parity check on the Leech lattice. The common aspect of these lattices is that they can be obtained via a single parity check or via the $k$ -ing construction. We exploit these constructions to introduce a new efficient paradigm for decoding. This leads to efficient list decoders and quasi-optimal decoders on the Gaussian channel. Both theoretical and practical performance (point error probability and complexity) of the new decoders are provided. [ABSTRACT FROM AUTHOR]
- Subjects :
- ERROR probability
LEECHES
LATTICE theory
GAUSSIAN channels
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 68
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 156419293
- Full Text :
- https://doi.org/10.1109/TIT.2022.3148196