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

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

doi:10.1007/978-3-030-61303-7_6

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

Electronic Engineering

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

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 π_A and elementary divisor construction (a.k.a. Construction π_D). 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 π_A. 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 language	English
Title of host publication	Mathematical Engineering
Editors	Victor Beresnevich, Alister Burr, Bobak Nazer, Sanju Velani
Publisher	Springer
Pages	201-240
ISBN (Electronic)	978-3-030-61303-7
ISBN (Print)	978-3-030-61302-0, 978-3-030-61305-1
DOIs	https://doi.org/10.1007/978-3-030-61303-7_6
Publication status	Published - 2020

Publication series

Name	Mathematical Engineering
ISSN (Print)	2192-4732
ISSN (Electronic)	2192-4740

Bibliographical note

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

Access to Document

10.1007/978-3-030-61303-7_6

Cite this

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title = "Multilevel Lattices for Compute-and-Forward and Lattice Network Coding",

abstract = "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.",

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Y1 - 2020

N2 - 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.

AB - 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.

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

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Network coded modulation for next generation wireless access networks

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

Abstract

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Bibliographical note

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Network coded modulation for next generation wireless access networks

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