Personal and Ubiquitous Computing

, Volume 23, Issue 5–6, pp 943–959 | Cite as

Superposition modulation–based new structure of four-dimensional turbo code (4D-TC) using modified interleaver and its application in WiMAX & LTE systems

  • Subhabrata BanerjeeEmail author
  • Sudipta Chattopadhyay
Original Article


Performance estimations of various kinds of turbo codes (TCs) and their applications in modern communication systems have been emerged as one of the potential research areas in recent past. In this paper, a modified interleaver-driven binary 4-Dimensional Turbo Code (4D-TC) using superposition modulation (SM) technique has been projected to intensify the minimum hamming distance (MHD). MHD (dmin) of the proposed structure has been amplified by incorporating feedback polynomial in primitive form for a fixed interleaver length. Moreover, improved dmin has further been achieved by introducing a modified interleaver which has been used to ensure scattering and mixing operation on the incoming bits in an appropriate manner. Furthermore, upper bound of the proposed structure has been evaluated and comprehensive asymptotic behavior of the proposed code has been analyzed in terms of dmin by adopting two analytical approaches namely finite length rule and asymptotic spectral shape function. Finally, to prove the superiority of the proposed structure, a comparative study of the BER performance of different forms of TCs have been carried out in WiMAX under numerous fading settings. Moreover a comparative BER analysis has also been done in long term evolution (LTE) system as well.


BER Four-dimensional turbo code Interleaver Minimum hamming distance Spectral shape function 



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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electronics & Communication EngineeringFuture Institute of Engineering & ManagementKolkataIndia
  2. 2.Department of Electronics & Telecommunication EngineeringJadavpur UniversityKolkataIndia

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