Practical Decoders for Barnes-wall Lattice Constellations∗

EXTENDED ABSTRACT. In 2008, Micciancio and Nicolosi [1] have proposed a low-complexity algorithm to decode the infinite Barnes-Wall lattice BW2m ⊂ C2m for any m ≥ 1 such that the worst-case complexity is O ( N log(N) ) where N = 2. More recently, Construction A′ [2] of Barnes-Wall lattices has been proposed wherein the BW2m can be obtained as BW2m = (1+ i) mZ[i]2m ⊕L2m such that L2m is a cubic-shaped lattice constellation. Inspired by the existence of the low-complexity Barnes-Wall lattice decoder, in this paper, we study the error performance of L2m as a coded modulation scheme for AWGN channels. To encode the code, we use Construction A′, and to decode the code we use the infinite Barnes-Wall lattice decoder (IBWD) [1]. First, we study the error performance of IBWD in decoding the infinite lattice and then propose a variant of it called the Barnes-Wall lattice constellation decoder (BWCD) to decode the lattice constellation. We also present simulation results on the bit error rate of the decoders.