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On the decoding of lattices constructed via a single parity check

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 is constructed as a simple application of single parity-check principle on the Leech lattice. The common aspect of these lattices is that they can be obtained via a single parity check or via the king 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.
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https://hal.archives-ouvertes.fr/hal-03700945
Contributor : Philippe CIBLAT Connect in order to contact the contributor
Submitted on : Tuesday, June 21, 2022 - 3:17:11 PM
Last modification on : Sunday, June 26, 2022 - 12:35:15 PM

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Vincent Corlay, Joseph J Boutros, Philippe Ciblat. On the decoding of lattices constructed via a single parity check. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2022, 68 (5), pp.2951 - 2968. ⟨10.1109/TIT.2022.3148196⟩. ⟨hal-03700945⟩

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