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Distance Spectrum of Fixed-Rate Raptor Codes with Linear Random Precoders

Lázaro Blasco, Francisco and Paolini, Enrico and Liva, Gianluigi and Bauch, Gerhard (2016) Distance Spectrum of Fixed-Rate Raptor Codes with Linear Random Precoders. IEEE Journal on Selected Areas in Communications, 34 (2), pp. 422-436. IEEE - Institute of Electrical and Electronics Engineers. DOI: 10.1109/JSAC.2015.2504281 ISSN 0733-8716

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Official URL: http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=7339429


Raptor code ensembles with linear random outer codes in a fixed-rate setting are considered. An expression for the average distance spectrum is derived and this expression is used to obtain the asymptotic exponent of the weight distribution. The asymptotic growth rate analysis is then exploited to develop a necessary and sufficient condition under which the fixed-rate Raptor code ensemble exhibits a strictly positive typical minimum distance. The condition involves the rate of the outer code, the rate of the inner fixed-rate Luby Transform (LT) code and the LT code degree distribution. Additionally, it is shown that for ensembles fulfilling this condition, the minimum distance of a code randomly drawn from the ensemble has a linear growth with the block length. The analytical results can be used to make accurate predictions of the performance of finite length Raptor codes. These results are particularly useful for fixed-rate Raptor codes under maximum likelihood erasure decoding, whose performance is driven by their weight distribution.

Item URL in elib:https://elib.dlr.de/104959/
Document Type:Article
Title:Distance Spectrum of Fixed-Rate Raptor Codes with Linear Random Precoders
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Lázaro Blasco, FranciscoDLRUNSPECIFIED
Paolini, EnricoUniv. of BolognaUNSPECIFIED
Date:February 2016
Journal or Publication Title:IEEE Journal on Selected Areas in Communications
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In ISI Web of Science:Yes
DOI :10.1109/JSAC.2015.2504281
Page Range:pp. 422-436
Publisher:IEEE - Institute of Electrical and Electronics Engineers
Keywords:Fountain codes, Raptor codes, erasure correction, maximum likelihood decoding.
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Communication and Navigation
DLR - Research area:Raumfahrt
DLR - Program:R KN - Kommunikation und Navigation
DLR - Research theme (Project):R - Vorhaben Multimedia Satellitennetze
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Communication and Navigation > Satellite Networks
Deposited By: Lazaro Blasco, Francisco
Deposited On:06 Jul 2016 16:06
Last Modified:31 Jul 2019 20:02

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