"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki ISSN 1684-1719, N 5, 2018

contents of issue      DOI  10.30898/1684-1719.2018.5.1     full text in Russian (pdf)  


L. E. Nazarov, P. V. Shishkin
Fryazinio Branch of Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences, Vvedensky Sq.1, Fryazino Moscow region 1411
90, Russia

 The paper is received on April 16, 2018


Abstract. The theme of this paper is investigation of the characteristics of error-correcting block turbo-codes which enable communication at relatively low received signal/noise and provide very high power efficiency. Specific feature of investigated turbo-codes is construction with application of low-density parity-check codes (LDPC) and these turbo-codes are LDPC too. According to this fact the considered block turbo-codes have symbol-by-symbol decoding algorithms developed for common class LDPC codes, namely, BP (belief propagation) and BP modification (mBP) decoding algorithms. The BP and mBP decoding algorithms are iterative and for implementation the signal/noise is not required. The resulted characteristics of block turbo-codes constructed with application of LDPC based on finite Eucledean and projective geometries (namely, duration of code words, information volume, code rate, error performances) are presented. 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 the mBP decoding algorithm is more effective than BP decoding algorithm (difference between signal/noise is more 0.2 dB). The simulations have shown that the error performances of investigated turbo-codes are better than that for convolutional codes with equivalent code rate 1/3, the degradation is about 2 dB for bit-error 0.00001.

Key words: block product codes, 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, 560 p.

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

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

4 Nazarov L.E., Batanov V.V., Kuznezov O.O. Symbol-by-symbol iterative decoding algorithms for turbo-codes based on single-parity-check codes. Zhurnal Radioelectroniki - Journal of Radio Electronics,  2014, No. 9, Avaiable at: http://jre.cplire.ru/jre/sep14/1/text.pdf (In Russian)

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

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

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

8. Golovkin I.V., Nazarov L.E. The development and realization of block turbo-codes decoding. Zifrovaja obrabotka signalov – Digital Signal Processing. 2009, No. 4. pp. 37-40 (In Russian)

9. 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]. Ěoscow, Radio I Svyaz Publ.,  1985 (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, pp.415-421

11. Tanner R.M. A recursive approach to low complexity codes.  IEEE Transactions on Information Theory. 1981, Vol. 27, No. 9, pp. 533-547

12. Nazarov L.E., Sheglov M.A. The error-performances of symbol-by-symbol iterative decoding algorithms for signals based on low-density parity-check codes.  Zhurnal Radioelectroniki - Journal of Radio Electronics,  2015, No. 4, Avaiable at: http://jre.cplire.ru/jre/apr15/5/text.pdf.


For citation:
L. E. Nazarov, P. V. Shishkin. The investigation of characteristics of error-correcting block turbo-codes based on low-density parity-checked codes. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2018. No. 5. Available at http://jre.cplire.ru/jre/may18/1/text.pdf

DOI  10.30898/1684-1719.2018.5.1