On the Decoding of Lattices Constructed via a Single Parity Check

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 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.