Page 52 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 6 – Wireless communication systems in beyond 5G era
P. 52

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 6




              a  pseudo‑Deepcode  by  replacing  the            [3] D. J. C. MacKay, “Good error correcting codes based
          Deepcode modulator with a modulator of order    = 4.      on very sparse matrices”, IEEE Transactions on In‑
          Results  show  that  the  DEF‑LSTM  code  has  better     formation Theory, vol. 45, no. 2, pp. 399‑431, Mar.
          performance  compared  to  the  pseudo‑Deepcode  as  its   1999.
          BLER  is  signi icantly  lower  in  the  whole  range  of  SNR that
                                                                [4] C. Berrou, A. Glavieux and P. Thitimajshima, “Near
          we  evaluated.  The  DEF‑LSTM  code  BLER  gain  over
                                                                    Shannon limit error‑correcting coding and decod‑
          pseudo‑Deepcode is larger than one order of magnitude
                                                                    ing: turbo‑codes,” International Conference on Com‑
          for  SNR=5  dB  and  6  dB.  Moreover,  the  DEF‑LSTM  code
                                                                    munications, ICC’93,Geneva, Switzerland, pp. 1064‑
          outperforms  NR  LDPC  (dashed  black  curve)  by  at  least
                                                                    70, May 1993.
          three orders of magnitude BLER for SNR ≥ 4 dB.
                                                                [5] S. Lin, D. Costello, Error Control Coding, Prentice‑
          5.  CONCLUSION AND FURTHER WORK                           Hall, Englewood Cliffs, NJ: 1983, 2011.
                                                                [6] Y. Polyanskiy, H. V. Poor and S. Verdú, “Feedback in
          A  new  deep  neural  network‑based  error  correction  en‑
                                                                    non‑asymptotic regime,” IEEE Transactions on Infor‑
          coder architecture for channels with feedback has been
                                                                    mation Theory,, vol. 57, no. 8, pp. 4903‑4925, Aug.
          presented.  The  new  architecture  generates parity  sym‑
                                                                    2011.
          bols  based  on  feedbacks  in  longer  time  windows  com‑
          pared  to  prior  architectures,  thereby  introducing  long‑
                                                                [7] J. Schalkwijk, “A coding scheme for additive noise
          range dependencies between parity symbols within each     channels with feedback‑I: No bandwidth con‑
          codeword.
                                                                    straint,” IEEE Transactions on Information Theory,
          It has been shown that the codes designed according to    vol. 12, no. 2, pp. 172‑182, Aug. 1966.
          the DEF architecture achieve lower error rates than any
          other code designed for channels with feedback. As long‑   [8] M. Horstein, “Sequential transmission using noise‑
          range  dependencies  between  parity  symbols  are  a  nec‑   less feedback,” IEEE Transactions on Information
          essary ingredient of all good error correction codes, it is   Theory, vol. 9, no. 3, pp. 136‑143, July 1963.
          expected that further performance improvements can be
                                                                [9] J. M. Ooi and G. W. Wornell, “Fast iterative coding
          obtained  by  increasing  the  length  of  the  feedback  time
          windows.                                                  techniques for feedback channels,” IEEE Transac‑
                                                                    tions on Information Theory,, vol. 44, no. 7, pp. 2960‑
          Moreover,  by  a  suitable  selection  of  the  modulation  or‑
                                                                    2976, Nov. 1998.
          der,  we  showed  that  these  codes  can  adapt  to  the
          forward   channel   quality,   thereby   providing   the   [10] Z. Ahmad, Z. Chance, D. J. Love and C. Wang, “Con‑
          maximum  spectral  ef iciency  that  is  attainable  for  the   catenated coding using linear schemes for Gaussian
          given forward channel quality.                            broadcast channels with noisy channel output feed‑
          In this work, DEF codes have been designed and evaluated   back,” IEEE Transactions on Communications, vol. 63,
          for  forward  channels  impaired  by  additive  white  Gaus‑   no. 11, pp. 4576‑4590, Nov. 2015.
          sian noise and noiseless feedback, where the forward SNR
                                                               [11] K. Vakilinia, S. V. S. Sudarsan, V. S. Ranganathan,
          has been assumed to be perfectly known at design time
                                                                    D. Divsalar and R. D. Wesel, “Optimizing transmis‑
          (NN training) and during LLS. Code design with imperfect
                                                                    sion lengths for limited feedback with non‑binary
          SNR knowledge and evaluations in more realistic scenar‑
                                                                    LDPC examples,” IEEE Transaction on communica‑
          ios, such as channels with fading and noisy feedback, are
                                                                    tions, vol. 64, no. 6, pp. 2245‑2257, June 2016.
          interesting subjects that will need to be addressed in or‑
          der to make these codes applicable in real transmission   [12] Huawei, HiSilicon, “Performance evaluation of LDPC
          systems.  However, these topics require further thorough   codes for NR eMBB data,” R1‑1713740, 3GPP RAN1
          investigation and therefore are left for future works.    meeting #90, Prague, Czech Republic, August21–25,
                                                                    2017.
          REFERENCES
           [1] H.  Kim,  Y .  Jiang,  S.  Kannan,  S.  Oh,  P .  Viswanath,
              “Deepcode: feedback codes via deep learning,” IEEE
              Journal on Selected Areas in Information Theory, vol.
              1, no. 1, pp. 194‑206, May 2020.
           [2] E. Arikan, “Channel polarization:  a method for con‑
              structing  capacity‑achieving  codes  for  symmetric
              binary‑input memoryless channels,”  IEEE Transac‑
              tions on Information Theory, vol. 55, no. 7, pp. 3051‑
              3073, July 2009.






          40                                 © International Telecommunication Union, 2021
   47   48   49   50   51   52   53   54   55   56   57