On the decoding of lattices constructed via a single parity check

Vincent Corlay; Joseph J. Boutros; Philippe Ciblat; Loïc Brunel

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arXiv · 2012.06894

On the decoding of lattices constructed via a single parity check

Vincent Corlay·Joseph J. Boutros·Philippe Ciblat·Loïc Brunel

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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 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.

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Vincent Corlay, Joseph J. Boutros, Philippe Ciblat, Loïc Brunel. 2020-12-12. On the decoding of lattices constructed via a single parity check. https://arxiv.org/abs/2012.06894

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