V.V. Zolotarev – Dr.Sc.(Eng.), Professor, Senior Research Scientist, 

Space Research Institute of RAS (Moscow)

E-mail: zolotasd@yandex.ru

N.N. Grinchenko – Ph.D.(Eng.), Associate Professor, Department of Computer, 

Ryazan State Radio Engineering University

E-mail: grinchenko_nn@mail.ru

G.V. Ovechkin – Dr.Sc.(Eng.), Associate Professor, Professor, Department «Computing and Applied Mathematics»,  Ryazan State Radio Engineering University

E-mail: g_ovechkin@mail.ru

Multithreshold decoding (MTD) self-orthogonal codes (SOC) for erasure channels implementing optimization error-correction methods based on searching global extremum of functions in discrete spaces are considered. It is discussed the difficulty in providing low unrecovered erasures probability with using MTD at high noise level due need to using codes with high code distance.

To increase the efficiency of erasure recoveries the concatenated codes comprising inner self-orthogonal codes as well as outer codes being simple for decoding such as parity check codes, Hamming codes or BCH codes are offered. The usage of the codes offered provides efficient erasure recovery when operating near channel capacity with linear decoder complexity. For the codes low boundary for unrecovered erasures probability was offered. This boundary shows possibility to lower unrecovered erasures probability on 3…5 decimal orders in comparison with constituent SOC and is consistent with presented simulation results. It allows to use the boundary for estimate concatenated scheme performance at very low target unrecovered erasures probability. It is shown the submitted concatenated codes can provide effective erasure recovery near channel capacity at linear implementation complexity. It is unavailable for other erasure recovering methods. The paper discuss aspects of MTD software implementation with using GPU also. It is shown developed decoders provide decoding rate about several hundred megabytes per secound on GPU NVidea GeForce GTX 1060. Such rate allows to use software MTD in high throughput soft-oriented systems.

1. Fossorier M., Declerq D., Biglieri E. and others. Channel Coding: Theory, Algorithms, and Applications.  Academic Press Library in Mobile and Wireless Communications, Elsevier. 2014. 690 p.
2. Arıkan E. Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels. IEEE Trans. Inf. Theory. Jule 2009. V. 55. № 7. P. 3051−3073.
3. Pfister H.D., Sason I., Urbanke R. Capacity-achieving ensembles for the binary erasure channel with bounded complexity. IEEE Trans. Inform. Theory. 2005. V. 51. № 7. P. 2352−2379.
4. Pfister H.D., Sason I. Accumulate-Repeat-Accumulate Codes: Systematic Codes Achieving the Binary Erasure Channel Capacity with Bounded Complexity. IEEE Transactions on Information Theory. 2005.
5. Zolotarev V.V., Zubarev Yu.B., Ovechkin G.V. Mnogoporogovye dekodery i optimizatsionnaya teoriya kodirovaniya. Pod red. akademika RAN V.K. Levina. M.: Goryachaya liniya – Telekom. 2012. 238 s.
6. Zolotarev V.V., Ovechkin G.V., Chulkov I.V., Ovechkin P.V., Averin S.V., Satybaldina D.Zh., Kao V.T. Obzor dostizhenii optimizatsionnoi teorii dlya sputnikovykh kanalov i sistem DZZ: 25 let razvitiya. Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa. 2017. T. 14. № 1. S. 9−24.
7. Zolotarev V.V., Ovechkin G.V., Ovechkin P.V. Effektivnye mnogoporogovye metody dekodirovaniya samoortogonalnykh kodov. Vestnik Ryazanskogo gosudarstvennogo radiotekhnicheskogo universiteta. 2017. Vyp. 60. S. 113−122.
8. Grinchenko N.N., Zolotarev V.V., Ovechkin G.V., Ovechkin P.V. Mnogoporogovoe dekodirovanie v kanalakh s mnogopozitsionnoi modulyatsiei. Vestnik Ryazanskogo gosudarstvennogo radiotekhnicheskogo universiteta. 2006. Vyp. 19. S. 179−[1].
9. Ullah M.A., Omura R., Sato T., Ogivara H. Multi-Stage Threshold Decoding for High Rate Convolutional Codes for Optical Communications. The 7th Advanced International Conference on Telecommunications (AICT-2011). 2011. P. 87−93.
10. Messi Dzh. Porogovoe dekodirovanie: Per. s angl. Yu.L. Sagalovicha. Pod red. E.L. Blokha. M.: Mir. 1966. 208 s.
11. Grinchenko N., Gromov A., Ovechkin G. Improving performance of multithreshold decoder over binary erasure channel. The 6th Mediterranean Conference on Embedded Computing (MECO). 2017. Including ECYPS 2017.
12. Kuznetsov N.A., Zolotarev V.V., Ovechkin G.V., Ovechkin P.V. Nedvoichnye mnogoporogovye dekodery i drugie metody korrektsii oshibok v simvolnoi informatsii. Radiotekhnika. 2010. № 6. S. 4−9.
13. Ovechkin G.V., Ovechkin P.V. Ispolzovanie nedvoichnogo mnogoporogovogo dekodera v kaskadnykh skhemakh korrektsii oshibok. Vestnik Ryazanskogo gosudarstvennogo radiotekhnicheskogo universiteta. 2009. Vyp. 30. S. 7−12.
14. Ovechkin G.V. Metody uluchsheniya effektivnosti mnogoporogovogo dekodera samoortogonalnykh kodov. Vestnik Ryazanskoi gosudarstvennoi radiotekhnicheskoi akademii. 2004. Vyp. 14. S. 54−58.
15. Zolotarev V.V., Ovechkin G.V., Ovechkin P.V., Egamberdiev E. Divergentnoe kaskadnoe mnogoporogovoe dekodirovanie svertochnykh kodov. Radiotekhnika. 2018. № 5. S. 23−29.
16. Zolotarev V.V., Ovechkin G.V., Ovechkin P.V. Programmnaya realizatsiya mnogoporogovykh dekoderov s ispolzovaniem GPU. Radiotekhnika. 2016. № 11. S. 90−96.
17. Web sites www.mtdbest.iki.rssi.ru and www.mtdbest.ru.