Performance Limits of Lattice Reduction over Imaginary Quadratic Fields with Applications to Compute-and-Forward

被引：0

作者：

Lyu, Shanxiang ^{[1
]}

Porter, Christian ^{[1
]}

Ling, Cong ^{[1
]}

机构：

[1] Imperial Coll London, Dept EEE, London SW7 2AZ, England

来源：

2018 IEEE INFORMATION THEORY WORKSHOP (ITW) | 2018年

关键词：

lattice reduction; algebraic; compute-and-forward;

D O I：

暂无

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Bases in the complex field, along with direct-sums defined by rings of imaginary quadratic integers, induce algebraic lattices. In this work, we examine the properties and reduction of such lattices. Focusing on algebraic Lenstra-Lenstra-Lovasz (ALLL) reduction, we show that to satisfy Lovasz's condition requires the ring to be Euclidean. The proposed algorithm can be used to design network coding matrices in compute-and-forward (C&F).

引用

页码：480 / 484

页数：5

共 50 条

[1] Lattice Reduction Over Imaginary Quadratic Fields
Lyu, Shanxiang
Porter, Christian
Ling, Cong
[J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2020, 68 : 6380 - 6393
[2] Adaptive Compute-and-Forward with Lattice Codes Over Algebraic Integers
Huang, Yu-Chih
Narayanan, Krishna R.
Wang, Ping-Chung
[J]. 2015 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), 2015, : 566 - 570
[3] Lattice Codes Based on Product Constructions over Fq2 with Applications to Compute-and-Forward
Huang, Yu-Chih
Narayanan, Krishna R.
[J]. 2013 IEEE INFORMATION THEORY WORKSHOP (ITW), 2013,
[4] On LLL lattice basis reduction over imaginary quadratic fields by introducing reduction parameters
Arimoto, Koichi
[J]. INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2020, 15 (02): : 611 - 619
[5] Reduction theory over quadratic imaginary fields
Fried, D
[J]. JOURNAL OF NUMBER THEORY, 2005, 110 (01) : 44 - 74
[6] Lattices Over Eisenstein Integers for Compute-and-Forward
Tunali, Nihat Engin
Huang, Yu-Chih
Boutros, Joseph J.
Narayanan, Krishna R.
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2015, 61 (10) : 5306 - 5321
[7] Lattices over Eisenstein Integers for Compute-and-Forward
Tunali, Nihat Engin
Narayanan, Krishna R.
Boutros, Joseph J.
Huang, Yu-Chih
[J]. 2012 50TH ANNUAL ALLERTON CONFERENCE ON COMMUNICATION, CONTROL, AND COMPUTING (ALLERTON), 2012, : 33 - 40
[8] Lattice Codes for the Compute-and-Forward Protocol: The Flatness Factor
Belfiore, Jean-Claude
[J]. 2011 IEEE INFORMATION THEORY WORKSHOP (ITW), 2011,
[9] CONSTRUCTION OF CLASS FIELDS OVER IMAGINARY QUADRATIC FIELDS AND APPLICATIONS
Cho, Bumkyu
Koo, Ja Kyung
[J]. QUARTERLY JOURNAL OF MATHEMATICS, 2010, 61 (02): : 199 - 216
[10] Simplified compute-and-forward and its performance analysis
Hejazi, Mohsen
Nasiri-Kenari, Masoumeh
[J]. IET COMMUNICATIONS, 2013, 7 (18) : 2054 - 2063

← 1 2 3 4 5 →