NDLI: Spectra and minimum distances of repeat multiple accumulate codes

Content Provider	IEEE Xplore Digital Library
Author	Fagnani, F. Ravazzi, C.
Copyright Year	2008
Description	Author affiliation: Dipt. di Mat., Politec. di Torino, Turin (Fagnani, F.; Ravazzi, C.)
Abstract	In this paper we consider ensembles of codes, denoted $RA^{m},$ obtained by a serial concatenation of a repetition code and m accumulate codes through uniform random inter-leavers. We analyze their average spectrum functions for each m showing that they are equal to 0 below a threshold distance $isin_{m}$ and positive beyond it. One of our main results is to prove that these average spectrum functions form a not-increasing sequence in m converging uniformly to a limit spectrum function which is equal to the maximum between the average spectrum function of the classical linear random ensemble and 0. As a consequence the sequence $isin_{m}$ converges to the Gilbert-Varshamov distance. A further analysis allows to conclude that the threshold distance $isin_{m}$ is indeed the typical distance of the ensemble $RA^{m}$ when the interleaver length goes to infinity. Combining the two results we are able to conclude that the typical distance of the ensembles $RA^{m}$ converges to the Gilbert-Varshamov bound.
Starting Page	77
Ending Page	86
File Size	334354
Page Count	10
File Format	PDF
ISBN	9781424426706
DOI	10.1109/ITA.2008.4601028
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-01-27
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Spectral shape Estimation Random access memory Probabilistic logic Distance measurement Encoding Iterative decoding
Content Type	Text
Resource Type	Article

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