Construction pi(A) and pi(D) Lattices: Construction, Goodness, and Decoding Algorithms

Yu-Chih Huang*, Krishna R. Narayanan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

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 F-p1 , ... , F-pL, respectively, and hence is referred to as Construction pi(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 pi(A) lattices is proposed and its achievable rate for the additive white Gaussian noise channel is analyzed. A generalization named Construction pi(D) is also investigated, which subsumes Construction A with codes over prime fields, Construction D, and Construction pi(A) as special cases.

Original languageEnglish
Pages (from-to)5718-5733
Number of pages16
JournalIEEE Transactions on Information Theory
Volume63
Issue number9
DOIs
StatePublished - Sep 2017

Keywords

  • Lattices
  • lattice codes
  • linear codes
  • COMPUTE-AND-FORWARD
  • EISENSTEIN INTEGERS
  • AWGN CHANNEL
  • COSET CODES
  • INTERFERENCE
  • PACKINGS
  • CAPACITY
  • ERROR

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