Construction $pi _{A}$ and $pi _{D}$ 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 φA. 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 φA lattices is proposed and its achievable rate for the additive white Gaussian noise channel is analyzed. A generalization named Construction φD is also investigated, which subsumes Construction A with codes over prime fields, Construction D, and Construction φA as special cases.

author list (cited authors)

  • Huang, Y., & Narayanan, K. R.

citation count

  • 14

publication date

  • January 2017