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Linear source coding over rings and applications
KTH, School of Electrical Engineering (EES), Communication Theory.
KTH, School of Electrical Engineering (EES), Communication Theory.ORCID iD: 0000-0002-7926-5081
2012 (English)In: 2012 Swedish Communication Technologies Workshop, Swe-CTW 2012, IEEE , 2012, 1-6 p.Conference paper, Published paper (Refereed)
Abstract [en]

This paper studies linear coding (LC) techniques in the setting of computing functions of correlated memoryless sources. Instead of linear mappings over finite fields, we consider using linear mappings over finite rings as encoders. It is shown that generally the region c×R, where c ≥ 1 is a constant and R is the Slepian-Wolf (SW) region, is achievable with LC over ring (LCoR) when the function to compute is the identity function. c = 1 if the ring used is a field. Hence, LCoR could be suboptimal in terms of achieving the best coding rates (the SW region) for computing the identity function. In spite of that, the ring version shows several advantages. It is demonstrated that there exists a function that is neither linear nor can be linearized over any finite field. Thus, LC over field (LCoF) does not apply directly for computing such a function unless the polynomial approach [1], [2] is used. On the contrary, such a function is linear over some ring. Using LCoR, an achievable region containing the SW region can be obtained for computing this function. In addition, the alphabet sizes of the encoders are strictly smaller than using LCoF. More interestingly, LCoF is not useful if some special requirement is imposed.

Place, publisher, year, edition, pages
IEEE , 2012. 1-6 p.
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-109295DOI: 10.1109/Swe-CTW.2012.6376282Scopus ID: 2-s2.0-84871886173ISBN: 978-146734763-1 (print)OAI: oai:DiVA.org:kth-109295DiVA: diva2:581176
Conference
2012 Swedish Communication Technologies Workshop (Swe-CTW), Lund, Sweden, October 24-26 2012
Funder
Swedish Research CouncilICT - The Next Generation
Note

QC 20130104

Available from: 2012-12-28 Created: 2012-12-28 Last updated: 2013-04-11Bibliographically approved

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Skoglund, Mikael

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CiteExportLink to record
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Citation style
  • apa
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Language
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  • Other locale
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Output format
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