Pergroup and joint optimization of max-dmin precoder for MIMO with LDPC coding using QAM modulation




MIMO, LDPC, Tx-CSI, max-dmin precoder, SM, BER


MIMO technology not only offers diversity and capacity gains, but also provides higher spectral efficiency and significant link reliability over SISO systems. Many methods are developed to exploit the diversity offered by multi-antenna systems such as Alamouti code and spatial multiplexing that do not require transmitter-side channel status information (Tx-CSI). Other power allocation optimization techniques, also known as precoding, require a full or partial Tx-CSI. These techniques aim to transform the signal before transmission according to different criteria, among which the minimal Euclidean distance seems to be very effective and continues to interest the researchers. Given perfect channel state information at both sides of the communication, we propose in this paper a novel design of wireless transmission schemes that joint the minimal Euclidean distance precoder and error correction coding based on the non-binary low-density parity-check code (NB-LDPC), to finally determine a power allocation optimization solution that adapts a linear precoding block to an NB-LDPC encoded MIMO transmission. In this paper we use a quadrature amplitude modulation (QAM), over a Rayleigh fading channel with a maximum likelihood detection. Simulations results in term of bit error rate confirmed that NB-LDPC codes are particularly well suited to be jointly used with precoding schemes based on the maximization of the minimum Euclidean distance criterion.

Author Biography

Sarra Mahi, Abou Beker Belkaid University

Tlemcen Telecommunication Laboratory


Strelkovskaya, I.V.; Grygoryeva, T.I.; Solovskaya, I.N. “Self-similar traffic in G/M/1 queue defined by the Weibull distribution,” Radioelectron. Commun. Syst., v.61, n.3, p.128, 2018. DOI:

Pokamestov, D.A.; Kryukov, Y.V.; Rogozhnikov, E.V.; Abenov, R.R.; Demidov, A.Y. “Concepts of the physical level of the fifth generation communications systems,” Radioelectron. Commun. Syst., v.60, n.7, p.285, 2017. DOI:

Morgado, A.; Huq, K.M.S.; Mumtaz, S.; Rodriguez, J. “A survey of 5G technologies: regulatory, standardization and industrial perspectives,” Digit. Commun. Netw., v.4, n.2, p.87, 2017. DOI:

TAROKH, V.; JAFARKHANI, H.; CALDERBANK, A.R. “Space-time block codes from orthogonal designs,” IEEE Trans. Inf. Theory, v.45, n.5, p.1456, 1999. DOI:

Kreyndelin, V.B.; Ben Rejeb, T.B.K. “Nonlinear iterative precoding algorithm for MIMO multiuser systems,” Radioelectron. Commun. Syst., v.60, n.10, p.449, 2017. DOI:

Jing, Q.; Wu, Jiajia. “Performance comparison of space-time block and trellis codes in the MIMO land mobile satellite channels,” Radioelectron. Commun. Syst., v.60, n.1, p.1, 2017. DOI:

Nhan, Nhat-Quang; Rostaing, Philippe; Amis, Karine; Collin, Ludovic; Radoi, Emanuel. “Complexity reduction for the optimization of linear precoders over random MIMO channels,” IEEE Trans. Commun., v.65, n.10, p.4205, 2017. DOI:

Telatar, E. “Capacity of multi-antenna Gaussian channels,” European Trans. Telecommun., v.10, n.6, p.585, Nov./Dec. 1999. DOI:

Stoica, P.; Ganesan, G. “Maximum-SNR spatial-temporal formatting designs for MIMO channels,” IEEE Trans. Signal Process., v.50, n.12, p.3036, 2002. DOI:

Sampath, H.; Stoica, P.; Paulraj, A. “Generalized linear precoder and decoder design for MIMO channels using the weighted MMSE criterion,” IEEE Trans. Commun., v.49, n.12, p.2198, 2001. DOI:

Rostaing, P.; Berder, O.; Burel, G.; Collin, L. “Minimum BER diagonal precoder for MIMO digital transmissions,” Signal Process., v.82, n.10, p.1477, 2002. DOI:

Scaglione, A.; Stoica, P.; Barbarossa, S.; Giannakis, G.B.; Sampath, H. “Optimal designs for space-time linear precoders and decoders,” IEEE Trans. Signal Process., v.50, n.5, p.1051, 2002. DOI:

Collin, L.; Berder, O.; Rostaing, P.; Burel, G. “Optimal minimum distance-based precoder for MIMO spatial multiplexing systems,” IEEE Trans. Signal Process., v.52, n.3, p.617, Mar. 2004. DOI:

Ngo, Q.-T.; Berder, O.; Scalart, P. “Minimum Euclidean distance based precoders for MIMO systems using rectangular QAM modulations,” IEEE Trans. Signal Process., v.60, n.3, p.1527, 2012. DOI:

Mahi, S.; Bouacha, A. “Behavior of the minimum Euclidean distance optimization precoders with soft maximum likelihood detector for high data rate MIMO transmission,” Int. J. Advanced Computer Sci. App., v.9, n.2, p.364, 2018. DOI:

Shannon, C.E. “A mathematical theory of communication,” Bell System Tech. J., v.27, n.4, p.623, 1948. DOI:

Shpylka, A.A.; Zhuk, S.Ya. “Decoding of convolutional codes on a sliding window during signal propagation in a multipath communications channel,” Radioelectron. Commun. Syst., v.53, n.9, p.497, 2010. DOI:

Gallager, R. “Low-density parity-check codes,” IRE Trans. Inf. Theory, v.8, n.1, p.21, 1962. DOI:

MacKay, D.J.C.; Neal, R.M. “Near Shannonlimit performance of low density parity check codes,” Electron. Lett., v.33, n.6, p.457, 1997. DOI:

Brink, S.T.; Kramer, G.; Ashikhmin, A. “Design of low-density parity-check codes for modulation and detection,” IEEE Trans. Commun., v.52, n.4, p.670, Apr. 2004, DOI:

Islam, M.R.; Hossain, Md.M.; Hoque, Md.A.; Islam, K.K.; Ullah, Md.S. “Low density parity check code in cooperative MIMO communication at wireless sensor network,” Radioelectron. Commun. Syst., v.54, n.7, p.359, 2011. DOI:

Deepa, T.; Kumar, R. “Performance evaluation of LDPC coded MIMO transceiver with equalization,” Proc. of Int. Conf. on Recent Trends in Information Technology, 25-27 Jul. 2013, Chennai, India. IEEE, 2013, p.147-151. DOI:

Hou, J.; Siegel, P.H.; Milstein, L.B. “Performance analysis and code optimization of low density parity- check codes on Rayleigh fading channels,” IEEE J. Selected Areas Commun., v.19, n.5, p.924, May 2001. DOI:

Iniya, S. “Pergroup precoding for MIMO with LDPC coding using QAM modulation,” Int. J. Innovative Res. Technol. Sci. Eng., v.2, n.3, Mar. 2016.

Chehade, T.; Collin, L.; Rostaing, P.; Radoi, E.; Bazzi, O. “Power allocation optimization: linear precoding adapted to NB-LDPC coded MIMO transmission,” Int. J. Antennas Propag., v.2015, ID 975139, 2015. DOI:

Perez-Cruz, F.; Rodrigues, M.R.D.; Verdu, S. “MIMO Gaussian channels with arbitrary inputs: optimal precoding and power allocation,” IEEE Trans. Inf. Theory, v.56, n.3, p.1070, 2010. DOI:

Digital Video Broadcasting (DVB); Second Generation Framing Structure, Channel Coding and Modulation Systems for Broadcasting, Interactive Services, News Gathering and other Broadband Satellite Applications (DVB-S2) [archive], ETSI EN 302 307, V1.2.1, April 2009.





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