Joint permutor analysis and design for multiple turbo codes

Summary, in English

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: Ching He; Michael Lentmaier; Daniel J. Costello Jr.; Kamil Zigangirov
• Department/s: Department of Electrical and Information Technology
• Publishing year: 2006
• Language: English
• Pages: 4068-4083
• Publication/Series: IEEE Transactions on Information Theory
• Volume: 52
• Issue: 9
• Links: http://dx.doi.org/10.1109/TIT.2006.879973
• Document type: Journal article
• Publisher: IEEE - Institute of Electrical and Electronics Engineers Inc.
• Topic: Electrical Engineering, Electronic Engineering, Information Engineering
• Keywords: turbo codes; multiple turbo codes; interleaver design
• Status: Published
• Research group: Telecommunication Theory
• ISBN/ISSN/Other: ISSN: 0018-9448