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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)
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author
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
2013-04-29 14:01:19
date last changed
2016-10-13 04:36:15
@misc{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},
  keyword      = {turbo codes,multiple turbo codes,interleaver design},
  language     = {eng},
  number       = {9},
  pages        = {4068--4083},
  publisher    = {ARRAY(0x78e1330)},
  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},
  volume       = {52},
  year         = {2006},
}