Improving bounds on the minimum Euclidean distance for block codes by inner distance measure optimization

Document type: Journal Articles
Article type: Original article
Peer reviewed: Yes
Author(s): Efraim Laksman, Håkan Lennerstad, Magnus Nilsson
Title: Improving bounds on the minimum Euclidean distance for block codes by inner distance measure optimization
Journal: Discrete Mathematics
Year: 2010
Volume: 310
Issue: 22 Special issue SI
Pagination: 3267-3275
ISSN: 0012-365X
Publisher: Elsevier
URI/DOI: 10.1016/j.disc.2010.04.025
ISI number: 000282900500029
Organization: Blekinge Institute of Technology
Department: School of Computing, School of Engineering - Dept. of Mathematics & Natural Sciences (Sektionen för datavetenskap och kommunikation, Sektionen för ingenjörsvetenskap - Avd.för matematik och naturvetenskap)
School of Computing S-371 79 Karlskrona, School of Engineering S-371 79 Karlskrona
+46 455 38 50 00
http://www.bth.se/com; http://www.bth.se/ing/
Language: English
Abstract: The minimum Euclidean distance is a fundamental quantity for block coded phase shift keying (PSK). In this paper we improve the bounds for this quantity that are explicit functions of the alphabet size q, block length n and code size | C |. For q = 8, we improve previous results by introducing a general inner distance measure allowing different shapes of a neighborhood for a codeword. By optimizing the parameters of this inner distance measure, we find sharper bounds for the outer distance measure, which is Euclidean. The proof is built upon the Elias critical sphere argument, which localizes the optimization problem to one neighborhood. We remark that any code with q = 8 that fulfills the bound with equality is best possible in terms of the minimum Euclidean distance, for given parameters n and | C |. This is true for many multilevel codes.
Subject: Mathematics\Discrete Mathematics
Keywords: Block code, Elias' bound, Metric, Minimal Euclidean distance, Phase shift keying
Edit