Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2020. No. 5


Full text in Russian (pdf)
Russian page


DOI https://doi.org/10.30898/1684-1719.2020.5.4

UDC 621.391.01




L. E. Nazarov, Z. T. Nazarova

Fryazino Branch of Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences, Vvedensky Sq.1, Fryazino Moscow region 141190, Russia


The paper is received on April 21, 2020


Abstract. The focus of this paper is directed towards the investigation of the characteristics of symbol-by-symbol iterative decoding algorithms for error-correcting block turbo-codes which enable communication at relatively low received signal/noise and provide high power efficiency. Specific feature of investigated turbo-codes is construction with usage of low-density parity-check codes (LDPC) and these turbo-codes are in the class of LDPC too. According to this fact the considered turbo-codes have symbol-by-symbol decoding algorithms developed for total class LDPC codes, namely BP (belief propagation) and modification (MIN_SUM_BP). The BP decoding algorithm is iterative and for implementation the signal/noise is required, for implementation of MIN_SUM_BP decoding algorithm the signal/noise is not required. The resulted characteristics of turbo-codes constructed with usage of LDPC based on Euclidean geometry (namely, duration of code words, information volume, code rate, error performances) are presented in this paper. These component LDPC codes are cyclic and have encoding and decoding algorithms with low complexity implementation. The computer simulations for encoding and iterative decoding algorithms for the number of turbo-codes with different code rate and information volumes are performed. The results of computer simulations have shown that MIN_SUM_BP decoding algorithm is more effective than BP decoding algorithm for AWGN channel concerning error-performances. For Relay channel these decoding algorithms are equivalent concerning error-performances.

Key words: block product codes, Euclidean low-density parity-check codes, iterative decoding.


1. Peterson W.W., Weldon E. J. Error-Correcting Codes. The MIT PRESS Cambridge, Massachusets and London, England. 1972. [Russian translation: Peterson U., Veldon E. Kodi ispravlyachie oshibki.] Moscow: Mir, 1976. 594 p.

2. Li J., Lin S., Abdel-Chaffar K., Ryan W.E., Costello D.J. Jr. LDPC Code Designs, Constructions, and Unification. Cambridge. University Press. United Kingdom, 2017.

3. Johnson S.J. Iterative Error Correction: Turbo, Low-Density Parity-Check and Repeat-Accumulate Codes. Cambridge: Univ. Press, 2010.

4. Zuko A.G., Falko A.I., Panfilov I.P., Banket V.L., Ivachenko P.V. Pomechoustoichivost i effectivnost system peredachi informacii [The noise-immunity and effectivness of system message transmission]. Ìoscow, Radio i Svyaz. 1985. (In Russian)

5. Pyndiah R.M. Near-optimum decoding of product-codes: block turbo-codes. IEEE Transactions on Communications. 1998. Vol.46. No.8. P.1003-1010.

6. Nazarov L.E., Golovkin I.V. Realization of block turbo-code iterative decoding algorithms. Zifrovaja obrabotka signalov - Digital Signal Processing. 2009. No.2 P.2-6. (In Russian)

7. Nazarov L.E., Shishkin P.V. The investigation of error-performances for block turbo-codes based on low density parity check codes of finite geometries. Zhurnal Radioelectroniki - Journal of Radio Electronics. 2018. No.5. Avaiable at: http://jre.cplire.ru/jre/may18/1/text.pdf. DOI: 10.30898/1684-1719.2018.5.1 (In Russian)

8. Kumar1 Ch. Ravi, K. Padmaraju K. Hard Decision Decoding Performance Improved Using Turbo Product Codes. International Journal of Engineering &Technology. 2018. Vol.7. P.228-231.

9. Nazarov L.E. Characteristics of block turbo-codes based on low density parity check codes].  Informacionnye tehnologii – Informtion Technologies. 2018. Vol.24. No.6. P.427-432. (In Russian)

10. Liu Z., Pados D.A. A decoding algorithms for finite-geometry LDPC codes. IEEE Transactions on Communications. 2005. Vol. 53. No.3. P.415-421.

11. MacKay D.J.C., Neal R.M. Near Shannon limit performance of low density parity check codes.  Electronics Letters. 1997. Vol.33. P.457-458.

12. Nazarov L.E., Sheglov M.A. Characteristics of Full and Shortened Immune-Noise LDPC Codes Based on Finite-Geometry. Uspechi sovremennoi radioelectriniki - Achievements of Modern Radio Electronics, 2017. No.6. P.23-30. (In Russian)

13. Dunin-Barkovskii IV, Smirnov NV. Teoriya veroyatnostei i matematicheskaya statistika v tekhnike [The theory of probabilities and mathematical statistic for technics]. Ìoscow, Gosizdatel’stvo nauchno-technicheskoi literatury. 1955. (In Russian) 


For citation:

Nazarov L.E., Nazarova Z.T. Algorithms for decoding error-correction block turbo-codes based on Euclidean geometry low-density parity-check codes. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2020. No. 5. Available at http://jre.cplire.ru/jre/may20/4/text.pdf.  DOI https://doi.org/10.30898/1684-1719.2020.5.4