Joint permutor analysis and design for multiple turbo codes
(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:
https://lup.lub.lu.se/record/3731684
- author
- He, Ching ; Lentmaier, Michael LU ; Costello Jr., Daniel J. and Zigangirov, Kamil LU
- organization
- publishing date
- 2006
- 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}},
}