A simple proof for the existence of 'good' pairs of nested lattices

Or Ordentlich; Uri Erez

doi:10.1109/EEEI.2012.6376989

A simple proof for the existence of 'good' pairs of nested lattices

Or Ordentlich^*, Uri Erez

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

13 Scopus citations

Abstract

This paper gives a simplified proof for the existence of nested lattice codebooks that allow to achieve the capacity of the additive white Gaussian noise channel. The proof is self-contained and relies only on basic probabilistic and geometrical arguments. An ensemble of nested lattices which is different than the one used in previous proofs is introduced. This ensemble, in addition to giving rise to a simple proof, can be easily generalized to an ensemble of nested lattices chains. As a result, the proof technique given here easily extends to showing the existence of 'good' chains of nested lattices.

Original language	English
Title of host publication	2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012
DOIs	https://doi.org/10.1109/EEEI.2012.6376989
State	Published - 2012
Externally published	Yes
Event	2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012 - Eilat, Israel Duration: 14 Nov 2012 → 17 Nov 2012

Publication series

Name	2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012

Conference

Conference	2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012
Country/Territory	Israel
City	Eilat
Period	14/11/12 → 17/11/12

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10.1109/EEEI.2012.6376989

Cite this

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title = "A simple proof for the existence of 'good' pairs of nested lattices",

abstract = "This paper gives a simplified proof for the existence of nested lattice codebooks that allow to achieve the capacity of the additive white Gaussian noise channel. The proof is self-contained and relies only on basic probabilistic and geometrical arguments. An ensemble of nested lattices which is different than the one used in previous proofs is introduced. This ensemble, in addition to giving rise to a simple proof, can be easily generalized to an ensemble of nested lattices chains. As a result, the proof technique given here easily extends to showing the existence of 'good' chains of nested lattices.",

author = "Or Ordentlich and Uri Erez",

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Ordentlich, O & Erez, U 2012, A simple proof for the existence of 'good' pairs of nested lattices. in 2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012., 6376989, 2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012, 2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012, Eilat, Israel, 14/11/12. https://doi.org/10.1109/EEEI.2012.6376989

A simple proof for the existence of 'good' pairs of nested lattices. / Ordentlich, Or; Erez, Uri.
2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012. 2012. 6376989 (2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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A simple proof for the existence of 'good' pairs of nested lattices

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