Flip Left-to-Right Approach Based Inverse Tree Interleavers for Unconventional Integrated OFDM-IDMA and SCFDMA-IDMA Systems

  • Manish YadavEmail author
  • Vinod Shokeen
  • Pramod Kumar Singhal


Several interleavers have been proposed for conventional interleave division multiple access (CIDMA) systems which provides a mean to control burst errors and to reduce multi user and multiple access interferences. However, CIDMA alone is incapable of completely removing inter-symbol interference and inter-carrier interference problems even in presence of such interleaver. In this paper, a recently developed novel interleaver i.e. ‘flip left–right approach based inverse-tree interleaver’ (FLRITI) or simply ‘inverse tree interleaver’, has been explored for two unconventional integrated interleave division multiple access techniques i.e. single carrier frequency division multiple access cum interleave division multiple access (SCFDMA-IDMA) and orthogonal frequency division multiplexing based interleave division multiple access (OFDM-IDMA). The results and analysis reveal that this unconventional integration of CIDMA with SCFDMA and OFDM techniques in presence of FLRITI improves the overall system performance in terms of bit-error rate, memory footprint and computation complexity. Therefore, it validates the worthiness of FLRITI as a competent interleaver for the communication systems to be used even beyond fourth generation.


Conventional interleave division multiple access (CIDMA) Single carrier frequency division multiple access (SCFDMA) Tree interleaver (TI) Orthogonal frequency division multiplexing (OFDM) Integrated IDMA (IIDMA) Interleave Division Multiple Access (IDMA) 

List of Symbols


Level of repetition coder


Total no. of users


kth specific user


Interleaving pattern for kth user


Input data sequence of kth user


Length of data sequence


Chip sequence for kth user

\(\widetilde{{x_{k} }}\)

Interleaved sequence of kth user


Sequence obtained after SCM and IFFT operations


M × M DFT matrix


Length of chip sequence and/or number of OFDM subcarriers


Length of cyclic prefix

\({{\uptau }}_{\text{d}}\)

Channel delay spread

\({{\uptau }}_{{{\text{e}}\left( { \hbox{max} } \right)}}\)

Maximum timing-error


Length of MAC


Resultant output of MAC


Received vector for kth user




M × M circular channel matrix


M × M circular time-shift matrix


Channel matrix


Diagonalized channel matrix


Noise plus interference component

\(e_{ESE }\)

Output of ESE

\(e_{DEC }\)

Output of DEC

\(\prod_{LR}^{ - 1}\)

Inverse interleaving pattern of sequence flipped left-to-right


Mother or reference interleaver



3rd Generation partnership project


Apriori probability


Additive white Gaussian noise


Beyond 4th generation


Bit error rate


Chip-by-chip detection


Code-division multiple access


Conventional interleave division multiple access


Cyclic prefix insertion


Cyclic prefix removal




Discrete Fourier transforms


De-mapping of subcarriers


Elementary signal estimator


Forward error correction


Fast Fourier transforms


Flip left-to-right approach based inverse tree interleavers


Intercarrier interference


Inverse discrete Fourier transform


Inverse fast Fourier transform


Interleave division multiple access


Integrated interleave division multiple access


Intersymbol interference


Inverse tree based interleaver


Inverse tree interleaver


Logliklihood ratio


Long-term evolution


Multiple access channel


Multiple access interference


Multiuser interference


Orthogonal frequency division multiplexing


Orthogonal frequency division multiplexing based interleave division multiple access


Peak-to-average power ratio


Pseudo noise


Probability of occurrence


Random interleavers


Single carrier frequency division multiple access based interleave division multiple access


Subcarrier mapping


Tree based interleaver


Tree interleaver



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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electronics and Communication Engineering, Amity School of Engineering and TechnologyAmity UniversityNoidaIndia
  2. 2.Department of Electronics and Communication Engineering, Amity Institute of Advanced Research and StudiesAmity UniversityNoidaIndia
  3. 3.Department of Electronics EngineeringMadhav Institute of Technology and Science (MITS)GwaliorIndia

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