Non-Binary Parallel Turbo LDPC Codes Associated with High Order Constellation

  IJRES-book-cover  International Journal of Recent Engineering Science (IJRES)          
  
© 2019 by IJRES Journal
Volume-6 Issue-6
Year of Publication : 2019
Authors : Latifa Mostari, Abdelmalik Taleb-Ahmed, Abdennacer Bounoua
DOI :    10.14445/23497157/IJRES-V6I6P101

Citation 

MLA Style :Latifa Mostari, Abdelmalik Taleb-Ahmed, Abdennacer Bounoua "Non-Binary Parallel Turbo LDPC Codes Associated with High Order Constellation" International Journal of Recent Engineering Science 6.6(2019):1-6. 

APA Style :Latifa Mostari, Abdelmalik Taleb-Ahmed, Abdennacer Bounoua, Non-Binary Parallel Turbo LDPC Codes Associated with High Order Constellation. International Journal of Recent Engineering Science, 6(6),1-6.

Abstract
Since the non-binary LDPC (Low-Density Parity-Check) codes offer better performance than binary LDPC codes for a system using high order constellations such as the QAM (Quadrature Amplitude Modulation), one proposes in this paper a high non-binary LDPC code, called a parallel nonbinary turbo LDPC code. It is obtained by a parallel concatenation of two identical regular non-binary LDPC codes, separated by an interleaver introducing the diversity through the turbo-code structure proposed by Berrou and others. Regular codes were used to avoid the complexity of irregular codes despite that they have better performance than the regular code. In our simulation, we evaluate overRayleigh and Gaussian channels, the performance of the proposed code combined with a 16-QAMusing Gray mapping. We show that the parallel non-binary turbo LDPC code outperforms a single non-binary LDPC code, with the same code length and code rate. Also, we note that its performance can be improved with the increase of two numbers of iterations: global iterations and iterations of non-binary LDPC codes.

Reference
[1] Shannon, C. E. (1948).A Mathematical Theory of Communication. Bell System Technical Journal, 27, 379-423 and 623-656.
[2] Elias, P. (1955).Coding for Noisy Channels. IRE Conv. Rec., 3(4), 37-46.
[3] Beermann, M., Monz, E., Schmalen, L. &Varyx, P. (2013).High-Speed Decoding of Non-Binary Irregular LDPC Codes Using GPUs. in Proc. IEEE SiPS.
[4] Moision, B. (2013). Decoding Complexity and Performance of Short-Block LDPC Codes Over GF (q).IPN Progress Report,42-194.
[5] Berrou, C., Glavieux, A. &Thitimajshima, P. (1993).Near Shannon Limit Error Correcting Coding and Decoding: Turbo-Codes. IEEE ICC`93, 1064-1070, Geneva.
[6] Pyndiah, R. (1998).Near Optimum Decoding of Product Codes: Block Turbo-Codes. IEEE Transactions on Communications, 46(8), 1003-1010.
[7] Gallager, R. G. (1962).Low-Density Parity-Check Codes. IEEE Transaction Information Theory, 8(1), 21–28.
[8] Gallager, R. G. (1963).Low-density parity-check codes. PhD dissertation, Department of Electrical Engineering, M.I.T., Cambridge, Mass.
[9] MacKay, D. J. C. & Neal, R. M. (1995).Good codes based on very sparse matrices in Cryptography and Coding, 5th IMA Conference.
[10] Sipser, M. &Spieleman, D. A. (1996).Expender Codes. IRE Transaction on Information Theory, 42(6), 1710-1722.
[11] Luby, M. G., Mitzenmachery, M., Shokrollahiz, M. A., Spielmanx, D. A. &Stemann, V. (1979).Practical LossResilient Codes," STOC`97 Proceedings of the twenty-ninth annual ACM symposium on Theory of Computing, 150-159.
[12] Davey, M. & MacKay, D. (2002).Low-Density Parity-Check Codes over GF(q). IEEE Communications Letters, 2(6), 165– 167.
[13] Barnault, L. &Declercq, D.(2003).Fast decoding algorithm for LDPC over GF(2q). In Information Theory Workshop Proceeding, 70-73.
[14] Wymeersch, H., Steendam, H. &Moeneclaey, M. (2004) .Log-domain decoding of LDPC codes over GF(q). in Proceeding IEEE International Conference Communication, 772-776, Paris, France.
[15] Spagnol, C., Popovici, E., &Marnane, W. (2009).Hardware implementation of GF(2m) LDPC decoders. IEEE Transactions Circuits Systems I, Reg. Papers, 56(12), 2609- 2620.
[16] Declercq, D., &Fossorier, M. (2007). Decoding Algorithms for Non-binary LDPC Codes over GF(q). IEEE Transactions on Communications. 55(4), 633-643.
[17] Voicila, A., Declercq, D., Verdier, F., Fossorier, M. &Urard, P. (2010).Low-Complexity Decoding for Non-Binary LDPC Codes in High Order Fields. IEEE Transactions on Communications, 58(5), 1365-1375.
[18] Rekha Rani. "Analytical Performance of LDPC Codes with OC in the Presence of Interferers", International Journal of Engineering Trends and Technology (IJRES), V12(3),136- 140 June 2014.
[19] Wang, C., Chen, X., Li, Z., & Yang, S. (2013).A Simplified Min-Sum Decoding Algorithm for Non-Binary LDPC Codes. IEEE Transactions on Communications, 61(1), 24–32.
[20] AlMuaini, S., AlDweik, A. &AlQutayri, M. (2013).BER Performance of Turbo Product LDPC Codes with NonSequential Decoding. Wireless and Mobile Networking Conference, 1-6.
[21] Hung, J., Shyu, J. & Chen, S. (2011).A New HighPerformance and Low-complexity Turbo-LDPC Code. International Conference on Multimedia and Signal Processing, 68-72.
[22] Kumar, R. P. &Kshetrimayum, R. S. (2013). An Efficient Methodology for Parallel Concatenation of LDPC Codes with Reduced Complexity and Decoding Delay," in Proceeding National Conference on Communications (NCC), New Delhi, India.
[23] Behairy, H. & Chang, S. C. (2000).Parallel Concatenated Gallager Codes. Electronics Letters, 36(24), 2025-2026.
[24] Behairy, H. M., &Benaissa, M. (2014).Multiple Parallel Concatenated Gallager Codes: Code Design and Decoding Techniques.IETE Journal of research, 59(20)
[25] Wang, C. L., Li, Z. & Yang, S. (2012). A New Min-Sum Based Decoding Algorithm for Non-Binary LDPC Codes. International Conference on Computing, Networking and Communications, Data Storage Technology and Applications Symposium, 476–480.
[26] Belgheit, B., Boukelif, A., Moulay, L. A. &Kamline M. (2012) . Parallel concatenated Gallager codes matrix and the effect of interleaver.International Journal of Electronics, 99(9), (pp. 1281-1289).
[27] Thuy V. Nguyen, Hung N. Dang and Hieu T. Nguyen"DelayLimited Rate-Compatible Protograph LDPC Codes" International Journal of Engineering Trends and Technology 67.7 (2019): 115-123.
[28] Mostari, L., Taleb-Ahmed, A. (2019) .Non-binary serial turbo LDPC codes combinedwithhighorder constellations.Journal of Science and Technology, 27(1), 33-47.
[29] Wang, Z. & Zhang, M. (2012) .A Serial Concatenated Scheme for LDPC Code to Achieve Better Error Correction Performance. 2nd International Conference on Cosumer Electronics, Communications and Networks, 1587-1589.
[30] Wu, K., Li, H. & Wang, Y. (1998) .The Influence of Interleaver on the Minimum Distance of Turbo-Code. International Conference on Communication Technology, 22- 24, China.
[31] Boutillon, E., Douillard, C. &Montorsi, G. (2007) .Iterative Decoding of Concatenated Convolutional Codes: Implementation Issues. Proceeding of IEEE, 95(6).
[32] Berrou, C. (2007) .Codes et Turbo-Codes. Springer.
[33] Boutros, J. J. (1998) .Les Turbo-Codes Parallèles et Séries. Polycopié de cours.
[34] Jiang, Y. (2010) . A Practical Guide to Error-Control Coding Using MATLAB. Artech House, 2010.
[35] Divsalar, D. &Pollara, F. (1995) .Multiple Turbo-Codes for Deep-Space Communications. Jet Propulsion Lab., Passadena, CA TDA Progress Repor,t 42-121.
[36] Hoeher, P. (1997) .New Iterative Turbo Decoding Algorithms. International Symposium on Turbo-Codes, 63- 70, Brest, France.
[37] Benedetto, S., Montorsi, G., Divsalar, D. &Pollara, F. (1996) .Soft-Output Decoding Algorithms in Iterative Decoding of Turbo-Codes. JPL TDA Progress Report, 42-124.
[38] Rekh, S., Rani, S. S. &Shanmugam, A. (2005) .Optimal Choice of Interleaver for Turbo-Codes. Academic Open Internet Journal, 15.
[39] P.Ravikiran and Mehul C. Patel, "Density Evolution of Low Density Parity Check codes over different channels" SSRG International Journal of VLSI & Signal Processing 4.2 (2017): 39-44.
[40] Mostari, L., Taleb-Ahmed, A. &Bounoua, A. (2018) .High performance LDPC codes for high spectral efficiency transmission.Internetworking Indonesia Journal, 10(1), 09-15.
[41] Savin, V. (2008).Min-Max Decoding for Non-Binary LDPC Codes. Proceeding IEEE International Symposium Information Theory, 960-964.

Keywords
Low-Density Parity-Check codes, turbo-code, parallel concatenation, non-binary, iterative decoding.