Lattice Structures of Precoders Maximizing the Minimum Distance in Linear Channels
(2015) In IEEE Transactions on Information Theory 61(2). p.908-916- Abstract
- This paper investigates linear precoding over nonsingular linear channels with additive white Gaussian noise, with lattice-type inputs. The aim is to maximize the minimum distance of the received lattice points, where the precoder is subject to an energy constraint. It is shown that the optimal precoder only produces a finite number of different lattices, namely perfect lattices, at the receiver. The well-known densest lattice packings are instances of perfect lattices, but are not always the solution. This is a counter-intuitive result as previous work in the area showed a tight connection between densest lattices and minimum distance. Since there are only finite many different perfect lattices, they can theoretically be enumerated... (More)
- This paper investigates linear precoding over nonsingular linear channels with additive white Gaussian noise, with lattice-type inputs. The aim is to maximize the minimum distance of the received lattice points, where the precoder is subject to an energy constraint. It is shown that the optimal precoder only produces a finite number of different lattices, namely perfect lattices, at the receiver. The well-known densest lattice packings are instances of perfect lattices, but are not always the solution. This is a counter-intuitive result as previous work in the area showed a tight connection between densest lattices and minimum distance. Since there are only finite many different perfect lattices, they can theoretically be enumerated offline. A new upper bound on the optimal minimum distance is derived, which significantly improves upon a previously reported bound, and is useful when actually constructing the precoders. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/5201206
- author
- Kapetanovic, Dzevdan ; Cheng, Hei Victor ; Mow, Wai Ho and Rusek, Fredrik LU
- organization
- publishing date
- 2015
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- MIMO, modulation, lattices
- in
- IEEE Transactions on Information Theory
- volume
- 61
- issue
- 2
- pages
- 908 - 916
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- wos:000348298400017
- scopus:84921491045
- ISSN
- 0018-9448
- DOI
- 10.1109/TIT.2014.2367004
- language
- English
- LU publication?
- yes
- id
- 728463a6-1250-4558-8d27-e84edd620f7a (old id 5201206)
- date added to LUP
- 2016-04-01 13:01:28
- date last changed
- 2022-03-13 21:44:43
@article{728463a6-1250-4558-8d27-e84edd620f7a,
abstract = {{This paper investigates linear precoding over nonsingular linear channels with additive white Gaussian noise, with lattice-type inputs. The aim is to maximize the minimum distance of the received lattice points, where the precoder is subject to an energy constraint. It is shown that the optimal precoder only produces a finite number of different lattices, namely perfect lattices, at the receiver. The well-known densest lattice packings are instances of perfect lattices, but are not always the solution. This is a counter-intuitive result as previous work in the area showed a tight connection between densest lattices and minimum distance. Since there are only finite many different perfect lattices, they can theoretically be enumerated offline. A new upper bound on the optimal minimum distance is derived, which significantly improves upon a previously reported bound, and is useful when actually constructing the precoders.}},
author = {{Kapetanovic, Dzevdan and Cheng, Hei Victor and Mow, Wai Ho and Rusek, Fredrik}},
issn = {{0018-9448}},
keywords = {{MIMO; modulation; lattices}},
language = {{eng}},
number = {{2}},
pages = {{908--916}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
series = {{IEEE Transactions on Information Theory}},
title = {{Lattice Structures of Precoders Maximizing the Minimum Distance in Linear Channels}},
url = {{http://dx.doi.org/10.1109/TIT.2014.2367004}},
doi = {{10.1109/TIT.2014.2367004}},
volume = {{61}},
year = {{2015}},
}