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Joint Permutor Analysis and Design for Multiple Turbo Codes

He, Ching and Lentmaier, Michael and Costello, Jr., Daniel J. and Zigangirov, Kamil Sh. (2006) Joint Permutor Analysis and Design for Multiple Turbo Codes. IEEE Transactions on Information Theory, 52 (9), pp. 4068-4083. DOI: 10.1109/TIT.2006.879973

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Official URL: http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=35459&arnumber=1683926&count=47&index=12

Abstract

In this paper, we study the problem of joint permutor analysis and design for J-dimensional multiple turbo codes with J constituent encoders, J>2. The concept of summary distance is extended to multiple permutors of size N and used as the design metric. Using the sphere-packing concept, we prove that the minimum length-2 summary distance (spread) D<sub>min,2</sub> is asymptoticly upper-bounded by O(N<sup>(J-1)/J</sup>). We also show that the asymptotic minimum length-2L summary distance D<sub>min,2L</sub> for the class of random permutors is lower-bounded by O(N<sup>(J-2)/J-ε</sup>), where ε>0 can be arbitrarily small. Then, using the technique of expurgating “bad” symbols, we show that the spread of random permutors can achieve the optimum growth rate, i.e., O(N<sup>(J-1)/J</sup>), and that the asymptotic growth rate of D<sub>min,2L</sub> can also be improved. The minimum length-2 and length- 4 summary distances are studied for an important practical class of permutors–linear permutors. We prove that there exist J-dimensional multiple linear permutors with optimal spread D<sub>min,2</sub>=O(N<sup>(J-1)/J</sup>). Finally, we present several joint permutor construction algorithms applicable to multiple turbo codes of short and medium lengths.

Item URL in elib:https://elib.dlr.de/44664/
Document Type:Article
Title:Joint Permutor Analysis and Design for Multiple Turbo Codes
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
He, ChingSeagate Technology, Pittsburgh, PAUNSPECIFIED
Lentmaier, MichaelUNSPECIFIEDUNSPECIFIED
Costello, Jr., Daniel J.University of Notre Dame, INUNSPECIFIED
Zigangirov, Kamil Sh.University of Notre Dame, INUNSPECIFIED
Date:September 2006
Journal or Publication Title:IEEE Transactions on Information Theory
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:Yes
Volume:52
DOI :10.1109/TIT.2006.879973
Page Range:pp. 4068-4083
Status:Published
Keywords:permutor, interleaver, multiple turbo code, minimum distance, summary distance, turbo code
HGF - Research field:Aeronautics, Space and Transport (old)
HGF - Program:Space (old)
HGF - Program Themes:W KN - Kommunikation/Navigation
DLR - Research area:Space
DLR - Program:W KN - Kommunikation/Navigation
DLR - Research theme (Project):W - Projekt GalileoNAV (old)
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Communication and Navigation > Communications Systems
Deposited By: Lentmaier, Dr. Michael
Deposited On:14 Sep 2006
Last Modified:27 Apr 2009 13:04

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