Publisher DOI: 10.1109/JSAC.2015.2504281
Title: Distance Spectrum of Fixed-Rate Raptor Codes with Linear Random Precoders
Language: English
Authors: Lazaro, Francisco 
Paolini, Enrico 
Liva, Gianluigi 
Bauch, Gerhard 
Keywords: erasure correction;Fountain codes;Raptor codes
Issue Date: Feb-2016
Source: IEEE Journal on Selected Areas in Communications 2 (34): 7339429 (2016-02)
Journal or Series Name: IEEE journal on selected areas in communications 
Abstract (english): 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.
ISSN: 0733-8716
Institute: Nachrichtentechnik E-8 
Type: (wissenschaftlicher) Artikel
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