We employ polar codes as the building blocks of Construction D to construct lattices for the additive white Gaussian noise (AWGN) channel. The construction of these component polar codes is based on the idea of Pedarsani et al. for binary-input memoryless symmetric (BMS) channels. Our lattice construction takes the advantage of the performance gain of polar codes over Reed-Muller codes. Simulation results show the lattices constructed from polar codes outperform the benchmark Barnes-Wall lattices, which are constructed from Reed-Muller codes.
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