Multilevel Lattices for Compute-and-Forward and Lattice Network Coding

Yi Wang*, Yu Chih Huang, Alister G. Burr, Krishna R. Narayanan

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter


This work surveys the recent progresses in construction of multilevel lattices for compute-and-forward (C&F) and lattice network coding (LNC). This includes Construction πA and elementary divisor construction (a.k.a. Construction πD). Some important properties such as kissing numbers, nominal coding gains, goodness of channel coding, and efficient decoding algorithms of these constructions are also discussed. We then present a multilevel framework of C&F where each user adopts the same nested lattice codes from Construction πA. The achievable computation rate of the proposed multilevel nested lattice codes under multistage decoding is analyzed. We also study the multilevel structure of LNC, which serves as the theoretical basis for solving the ring-based LNC problem in practice. Simulation results show the large potential of using iterative multistage decoding to approach the capacity.

Original languageEnglish
Title of host publicationMathematical Engineering
EditorsVictor Beresnevich, Alister Burr, Bobak Nazer, Sanju Velani
ISBN (Electronic)978-3-030-61303-7
ISBN (Print)978-3-030-61302-0, 978-3-030-61305-1
Publication statusPublished - 2020

Publication series

NameMathematical Engineering
ISSN (Print)2192-4732
ISSN (Electronic)2192-4740

Bibliographical note

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

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