Inner Distance Measure Bounds on the Minimal Euclidean Distance for Symmetric PSK Block Codes

Document type: Conference Papers
Peer reviewed: Yes
Author(s): Efraim Laksman, Håkan Lennerstad, Magnus Nilsson
Title: Inner Distance Measure Bounds on the Minimal Euclidean Distance for Symmetric PSK Block Codes
Translated title: Gränser för minimala euklidiska avståndet för symmetriska blockkoder med inre avståndsmått
Conference name: 9th International Conference on Finite Fields and their Applications
Year: 2009
City: Dublin, Irland
Organization: Blekinge Institute of Technology
Department: School of Engineering - Dept. of Mathematics & Natural Sciences (Sektionen för ingenjörsvetenskap - Avd.för matematik och naturvetenskap)
School of Engineering S-371 79 Karlskrona
+46 455 38 50 00
http://www.bth.se/ing/
Authors e-mail: hln@bth.se
Language: English
Abstract: The minimum Euclidean distance is a fundamental quantity for block-coded PSK. In this paper improvements are made of bounds for this quantity that are explicit functions of the alphabet size q, block length n and code size |C|. Earlier work, where the restriction q=8 was used, is continued by a generalisation allowing any q.
The bound generalizes Elias critical sphere argument, which localizes the optimization problem to one neighbourhood, by use of so called inner distance measure for defining the shape of a sphere. Remark that codes which fulfill the bound with equality exist, and are best possible in terms of minimum Euclidean distance, for given parameters q, n and |C|.
Summary in Swedish: Minimala euklidiska avståndet är en fundamental storhet för en blockkod C. I detta papper görs förbättrade gränser för denna storhet som är explicita i de tre parametrarna alfabet storlek q, ordlängd n och kodstorlek c. Vi generaliserar Elias sfärargument genom att optimera ett inre avståndsmått så att vi får bästa tänkbara gräns för Euklidiskt avstånd.
Subject: Telecommunications\Coding Theory
Mathematics\General
Keywords: block code, Elias sphere, Euclidean distance, phase shift keying
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