Construction of Capacity-Achieving Lattice Codes: Polar Lattices

Understand

In this paper, we propose a new class of lattices constructed from polar codes, namely polar lattices, to achieve the capacity $\frac{1}{2}\log(1+\SNR)$ of the additive white Gaussian-noise (AWGN) channel.

• Our construction follows the multilevel approach of Forney \textit{et al.}, where we construct a capacity-achieving polar code on each level.
• The component polar codes are shown to be naturally nested, thereby fulfilling the requirement of the multilevel lattice construction.
• We prove that polar lattices are \emph{AWGN-good}.