Product construction of lattices as error-correcting codes

Amir John Salomon; Ofer Amrani

doi:10.1109/TCOMM.2006.885054

Product construction of lattices as error-correcting codes

Amir John Salomon^*, Ofer Amrani

^*Corresponding author for this work

School of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

This letter investigates the so-called product lattice (PL) construction. A PL is obtained from two low-dimensional lattices by means of the Kronecker product. Fundamental properties, mainly those determining the performance of a lattice as an error-correcting scheme over a bandwidth-limited channel, are derived for PLs. Due to their special structure and properties, PLs can provide an attractive family of lattice codes of good performance/complexity tradeoffs.

Original language	English
Pages (from-to)	3-10
Number of pages	8
Journal	IEEE Transactions on Communications
Volume	55
Issue number	1
DOIs	https://doi.org/10.1109/TCOMM.2006.885054
State	Published - Jan 2007

Keywords

Barnes-Wall lattice
Coset codes
Lattice codes
Leech lattice
Product codes

Access to Document

10.1109/TCOMM.2006.885054

Cite this

@article{fdba0264602c4434b5e8e3aa793f4903,

title = "Product construction of lattices as error-correcting codes",

abstract = "This letter investigates the so-called product lattice (PL) construction. A PL is obtained from two low-dimensional lattices by means of the Kronecker product. Fundamental properties, mainly those determining the performance of a lattice as an error-correcting scheme over a bandwidth-limited channel, are derived for PLs. Due to their special structure and properties, PLs can provide an attractive family of lattice codes of good performance/complexity tradeoffs.",

keywords = "Barnes-Wall lattice, Coset codes, Lattice codes, Leech lattice, Product codes",

author = "Salomon, {Amir John} and Ofer Amrani",

note = "Funding Information: Paper approved by T.-K. Truong, the Editor for Coding Theory and Techniques of the IEEE Communications Society. Manuscript received August 23, 2005; revised January 31, 2006. This work was supported in part by the Yitzhak and Chaya Weinstein Research Institute for Signal Processing. This paper was presented in part at the IEEE International Symposium on Information Theory, Chicago, IL, 2004.",

year = "2007",

month = jan,

doi = "10.1109/TCOMM.2006.885054",

language = "אנגלית",

volume = "55",

pages = "3--10",

journal = "IEEE Transactions on Communications",

issn = "0090-6778",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "1",

}

TY - JOUR

T1 - Product construction of lattices as error-correcting codes

AU - Salomon, Amir John

AU - Amrani, Ofer

N1 - Funding Information: Paper approved by T.-K. Truong, the Editor for Coding Theory and Techniques of the IEEE Communications Society. Manuscript received August 23, 2005; revised January 31, 2006. This work was supported in part by the Yitzhak and Chaya Weinstein Research Institute for Signal Processing. This paper was presented in part at the IEEE International Symposium on Information Theory, Chicago, IL, 2004.

PY - 2007/1

Y1 - 2007/1

N2 - This letter investigates the so-called product lattice (PL) construction. A PL is obtained from two low-dimensional lattices by means of the Kronecker product. Fundamental properties, mainly those determining the performance of a lattice as an error-correcting scheme over a bandwidth-limited channel, are derived for PLs. Due to their special structure and properties, PLs can provide an attractive family of lattice codes of good performance/complexity tradeoffs.

AB - This letter investigates the so-called product lattice (PL) construction. A PL is obtained from two low-dimensional lattices by means of the Kronecker product. Fundamental properties, mainly those determining the performance of a lattice as an error-correcting scheme over a bandwidth-limited channel, are derived for PLs. Due to their special structure and properties, PLs can provide an attractive family of lattice codes of good performance/complexity tradeoffs.

KW - Barnes-Wall lattice

KW - Coset codes

KW - Lattice codes

KW - Leech lattice

KW - Product codes

UR - http://www.scopus.com/inward/record.url?scp=33847608256&partnerID=8YFLogxK

U2 - 10.1109/TCOMM.2006.885054

DO - 10.1109/TCOMM.2006.885054

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:33847608256

SN - 0090-6778

VL - 55

SP - 3

EP - 10

JO - IEEE Transactions on Communications

JF - IEEE Transactions on Communications

IS - 1

ER -

Product construction of lattices as error-correcting codes

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this