"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki ISSN 1684-1719, N 11, 2018

contents of issue      DOI  10.30898/1684-1719.2018.11.1     full text in Russian (pdf)  

Full and shortened low-density parity-checked codes based on finite geometries and their decoding algorithms

 

 L. E. Nazarov
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 October 25, 2018

 

Abstract. The theme of this paper is investigation of the characteristics of error-correcting low-density parity-check codes (LDPC) which enable communication at relatively low received signal/noise and provide very high power efficiency. Specific feature of investigated codes is construction of these by means of full LDPC code word and information volume shortening. According to this the broad class of LDPC codes is constructed with variety of code-rates and information volumes. The full (original) LDPC codes are based on the finite geometries (finite Eucledean and projective geometries). The decoding algorithms for that are symbol-by-symbol decoding 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 full and shortened low-density parity-check codes (namely, duration of code words, information volume, code rate, error performances) are presented. The original 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 mBP decoding algorithm is more effective than BP decoding algorithm (difference between signal/noise is more 0.2 dB). The results of encoding and decoding algorithm realization using FPGA VIRTEX-5SX are presented, in particularly, the information rate 200 Mb/s is achieved for generator clock 180 MHz and for 10 iterations.

Key words: noise-immunity, low-density parity-check codes, iterative decoding.

References

1. Peterson W.W., Weldon E. J. Error-Correcting Codes. The MIT PRESS Cambridge, Massachusets and London, England, 1972.

2. Johnson S.J. Iterative Error Correction: Turbo, Low-Density Parity-Check and Repeat-Accumulate Codes. Cambridge: Univ. Press, 2010, 356 p.

3. Gallager R.G. Low-density parity-check codes. IRE Transactions Information Theory. 1968, Vol. 8, pp. 21-28.

4. 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

5. Richardson T.J., Shokrollahi M.A., Urbanke R.L. Design of capacity-approaching irregular low-density parity-check codes. IEEE Transactions on Information Theory, 2001, Vol. 47, No. 2, pp. 619-637.

6. Nazarov L.E., Golovkin I.V. .. Iterative symbol-by-symbol decoding for signals based on low-density parity-check codes. Izvestia Vysshikh Uchebnych Zavedenii. Electronika - Proceedings of Universities. Electronics, 2007, No. 3, pp. 43-49 (In Russian)

7. Blahut R.E. Theory and Practice of Error Control Codes. Copyright by Adison-Wesley Publishing Company, Inc., 1983, 576 p.

8. Kou Y., Lin S., Fossorier M. Low-density parity-check codes based on finite geometries: a rediscovery and new results. IEEE Transactions on Information Theory, 2001, Vol. IT-47, No. 11, pp. 2711-2736.

9. Liu Z., Pados D.A. A Decoding Algorithm for Finite-Geometry LDPC Codes. IEEE Transactions on Communications, 2005, Vol. 53, No. 3, pp. 415-421.

10. 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. (In Russian)

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

12. Li Z., Chen L., Lin S., Fong W.H. Efficient Encoding of Quasi-Cyclic Low-Density Parity-Check Codes. IEEE Transactions on Communications, 2006, Vol. 54, No. 1. pp. 71-81.

13. Nazarov L.E., Shishkin P.V. The characteristics of error-correcting block turbo-codes based on low-density parity-check codes. Informacionnye tehnologii - Information Technologies, 2018, Vol. 24, No. 6, pp. 427-431. (In Russian)

14. Research and Development for Space Data System Standards. Low density parity check codes for use in near-earth and deep space applications. 2007. Experimental specification CCSDS 131.1-O-2. 44 p.

 

For citation:
L. E. Nazarov. Full and shortened low-density parity-checked codes based on finite geometries and their decoding algorithms. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2018. No. 11. Available at http://jre.cplire.ru/jre/nov18/1/text.pdf

DOI  10.30898/1684-1719.2018.11.1