Joint permutor analysis and design for multiple turbo codes

Ching He, Michael Lentmaier, Daniel J. Costello Jr., Kamil Zigangirov

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21 Citations (SciVal)


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.
Original languageEnglish
Pages (from-to)4068-4083
JournalIEEE Transactions on Information Theory
Issue number9
Publication statusPublished - 2006

Subject classification (UKÄ)

  • Electrical Engineering, Electronic Engineering, Information Engineering


  • turbo codes
  • multiple turbo codes
  • interleaver design


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