RESEARCH ARTICLE Concatenation of polar codes with three‐dimensional parity check (3D‐PC) codes to improve error performance over fading channels Ibrahim Beram Jasim | Oguz Bayat | Osman N. Ucan Department of Electrical and Computer Engineering, Altinbas University, Istanbul, Turkey Correspondence Ibrahim Beram Jasim, Department of Electrical and Computer Engineering, Altinbas University, Istanbul, Turkey. Email: ibrahim.jasim@ogr.altinbas.edu.tr. Summary In this paper, we concatenated of three‐dimensional parity check (3D‐PC) block and polar codes for improving error correction performance and bit error rate (BER). Three different sizes of 3D parity check blocks (4 × 4 × 4, 8 × 8 × 8, and 16 × 16 × 16) are used for polar code concatenation. The 4 × 4 × 4 block returns the best performance, but higher complexity of decoder is needed unlikely. The 8 × 8 × 8 has returned acceptable complexity and good performacne. The complexity of decoder is less in the case of 16 × 16 × 16 with slight performance. The performance of the 3D‐PC is reduced when the codewords length is increased. The experiment considered the presence of additive white Gaussian noise (AWGN) with Rayleigh and Rician fading envi- ronments. 3D‐PC and polar code concatenation is more precise with codewords of short length, whereas there is insufficient concatenation accuracy with longer codewords. The outcomes of this study contain comparison between AWGN, Rayleigh, and Rician environments. The AWGN is noticed to have a lesser negative impact on the performance of code. Furthermore, increasing the code length may slightly fill the gap of performance between the concatenated and none concatenated polar codes due to the impact of code length on parity check code performance. Simulation results showed the coding performance in case of the polar code with concatenation and without concatenation for different code lengths. Generally, the 3D‐PC polar code concatenation is drawn the optimal result in AWGN environments. KEYWORDS list decoding, parity check, polar codes, successive cancelation decoding, 3D parity check 1 | INTRODUCTION Error correction theories are of the most interesting and applied part of mathematics and informatics. Polar codes were invented by Erdal Arikan. At Arikan, 1 the author proposed achieving the memoryless channel capacity of binary input‐ discrete (BI‐DMC). In polar codes, small or moderate length of the codewords give temperate error correction perfor- mance. This is not impressive as other types of coding schemes, and the improvement is not significant over the AWGN channel in Eslami and Pishro‐Nik. 2 Therefore, the polar codes used concatenation technique with other code schemes to improve error correction performance for the entire system. In this paper, we introduce the 3D‐PC concatenation Received: 28 June 2018 Revised: 20 February 2019 Accepted: 3 March 2019 DOI: 10.1002/dac.3970 Int J Commun Syst. 2019;e3970. https://doi.org/10.1002/dac.3970 © 2019 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/dac 1 of 9