Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

Joint permutor analysis and design for multiple turbo codes

He, Ching ; Lentmaier, Michael LU ; Costello Jr., Daniel J. and Zigangirov, Kamil LU (2006) In IEEE Transactions on Information Theory 52(9). p.4068-4083
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) Dmin,2 is asymptoticly upper-bounded by O(N J-1/J). We also show that the asymptotic minimum length-2L summary distance Dmin,2L for the class of random permutors is lower-bounded by O(NJ-2J-epsi/), where epsi>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(NJ-1/J), and... (More)
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) Dmin,2 is asymptoticly upper-bounded by O(N J-1/J). We also show that the asymptotic minimum length-2L summary distance Dmin,2L for the class of random permutors is lower-bounded by O(NJ-2J-epsi/), where epsi>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(NJ-1/J), and that the asymptotic growth rate of Dmin,2L 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 Dmin,2 =O(NJ-1J/). Finally, we present several joint permutor construction algorithms applicable to multiple turbo codes of short and medium lengths. (Less)
Please use this url to cite or link to this publication:
author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
turbo codes, multiple turbo codes, interleaver design
in
IEEE Transactions on Information Theory
volume
52
issue
9
pages
4068 - 4083
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:33748560140
ISSN
0018-9448
DOI
10.1109/TIT.2006.879973
language
English
LU publication?
yes
id
b315da5c-22f6-417b-8fdb-983fba37de15 (old id 3731684)
date added to LUP
2016-04-04 09:44:18
date last changed
2022-01-29 19:21:10
@article{b315da5c-22f6-417b-8fdb-983fba37de15,
  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) Dmin,2 is asymptoticly upper-bounded by O(N J-1/J). We also show that the asymptotic minimum length-2L summary distance Dmin,2L for the class of random permutors is lower-bounded by O(NJ-2J-epsi/), where epsi>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(NJ-1/J), and that the asymptotic growth rate of Dmin,2L 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 Dmin,2 =O(NJ-1J/). Finally, we present several joint permutor construction algorithms applicable to multiple turbo codes of short and medium lengths.}},
  author       = {{He, Ching and Lentmaier, Michael and Costello Jr., Daniel J. and Zigangirov, Kamil}},
  issn         = {{0018-9448}},
  keywords     = {{turbo codes; multiple turbo codes; interleaver design}},
  language     = {{eng}},
  number       = {{9}},
  pages        = {{4068--4083}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Transactions on Information Theory}},
  title        = {{Joint permutor analysis and design for multiple turbo codes}},
  url          = {{http://dx.doi.org/10.1109/TIT.2006.879973}},
  doi          = {{10.1109/TIT.2006.879973}},
  volume       = {{52}},
  year         = {{2006}},
}