An upper bound on the minimum Euclidean distance for block-coded phase-shift keying

Document type: Journal Articles
Article type: Original article
Peer reviewed: Yes
Author(s): Magnus Nilsson, Håkan Lennerstad
Title: An upper bound on the minimum Euclidean distance for block-coded phase-shift keying
Journal: IEEE Transactions on Information Theory
Year: 2000
Volume: 46
Issue: 2
Pagination: 656-662
ISSN: 0018-9448
ISI number: 000085870000027
Organization: Blekinge Institute of Technology
Department: School of Engineering - Dept. Mathematics and Science (Sektionen för teknik – avd. för matematik och naturvetenskap)
School of Engineering S- 371 79 Karlskrona
+46 455 38 50 00
http://www.tek.bth.se/
Authors e-mail: magnus.g.nilsson@bth.se, hakan.lennerstad@bth.se
Language: English
Abstract: We present an upper bound on the minimum Euclidean distance d_{Emin}(C) valid for any linear and non-linear block coded PSK. There are several well known block codes that satisfy this upper bound with equality. With given parameters; the alphabet size q, the blocklength n and the number of codewords |C|, it therefore follows that these codes are best possible in terms of minimum Euclidean distance.
We furthermore establish a lower bound valid for Gray coded binary block codes. The minimum Euclidean distance is bounded from below by the minimum Hamming distance of the corresponding binary code. For several Gray coded binary block codes the upper and the lower bounds coincide. It can then be concluded without calculating the minimum Euclidean distance that these codes are best possible.
Subject: Telecommunications\Coding Theory
Signal Processing\Detection and Classification
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