Construction πA and πD Lattices: Construction, Goodness, and Decoding Algorithms
Yu-Chih Huang, Krishna R. Narayanan · IEEE Transactions on Information Theory · 2017
A novel construction of lattices is proposed. This construction can be thought of as a special class of Construction A from codes over finite rings that can be represented as the Cartesian product of L linear codes over Fp1,..., FpL, respectively, and hence is referred to as Construction πA. The existence of a sequence of such lattices that is good for channel coding (i.e., Poltyrev-limit achieving) under multistage decoding is shown. A new family of multilevel nested lattice codes based on Construction πAlattices is proposed and its achievable rate for the additive white Gaussian noise channel is analyzed. A generalization named Construction πDis also investigated, which subsumes Construction A with codes over prime fields, Construction D, and Construction πAas special cases.