Construction A and D Lattices: Construction, Goodness, and Decoding Algorithms Academic Article uri icon

abstract

  • 1963-2012 IEEE. 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 mathbb {F}-{p-{1}},ldots ,mathbb {F}-{p-{L}} , respectively, and hence is referred to as Construction A. 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 A lattices is proposed and its achievable rate for the additive white Gaussian noise channel is analyzed. A generalization named Construction D is also investigated, which subsumes Construction A with codes over prime fields, Construction D, and Construction A as special cases.

published proceedings

  • IEEE Transactions on Information Theory

author list (cited authors)

  • Huang, Y., & Narayanan, K. R.

citation count

  • 14

complete list of authors

  • Huang, Yu-Chih||Narayanan, Krishna R

publication date

  • August 2017