A Simpler Proof for the Existence of Capacity-Achieving Nested Lattice Codes

Renming Qi*, Chen Feng, Yu-Chih Huang

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Nested lattice codes have played an important role in network information theory. However, their achievability proofs are often involved, even for the case of the additive white Gaussian noise (AWGN) channel. In sharp contrast, their finite-field counterparts, nested linear codes, enjoy much simpler achievability proofs. In this paper, we present a simple and direct proof that nested lattice codes achieve the AWGN channel capacity. In particular, we make use of an intriguing connection between nested lattice codes and nested linear codes, which allows us to keep the proof as simple as that for nested linear codes.

Original languageEnglish
Title of host publication2017 IEEE INFORMATION THEORY WORKSHOP (ITW)
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages564-568
Number of pages5
ISBN (Electronic)9781509030972
DOIs
StatePublished - 2017
Event2017 IEEE Information Theory Workshop, ITW 2017 - Kaohsiung, Taiwan
Duration: 6 Nov 201710 Nov 2017

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2018-January
ISSN (Print)2157-8095

Conference

Conference2017 IEEE Information Theory Workshop, ITW 2017
CountryTaiwan
CityKaohsiung
Period6/11/1710/11/17

Keywords

  • AWGN CHANNEL
  • INTERFERENCE

Cite this

Qi, R., Feng, C., & Huang, Y-C. (2017). A Simpler Proof for the Existence of Capacity-Achieving Nested Lattice Codes. In 2017 IEEE INFORMATION THEORY WORKSHOP (ITW) (pp. 564-568). (IEEE International Symposium on Information Theory - Proceedings; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ITW.2017.8277953