Performance of Polar Codes over Generalized Correlated Fading Channels

Abstract

Polar coding, as introduced by Arikan in 2009, is an error correcting code scheme that uses the polarization technique to obtain almost noise-free channels that are suitable for transmission. Polar codes are being widely studied due to their applications on the 5th Generation (5G) of mobile communication systems. In 5G communications, the wireless channel is subject to fading that can significantly degrade the quality of the transmitted signals. In this context, the generalized fading models are useful due to their capacity to model a variety of channel conditions ranging from moderate to severe fading by adjusting some parameters. In this work, the authors investigate the performance of polar codes considering the transmission over generalized fading channels. Additionally, the effect of channel correlation is analyzed and a random interleaver is proposed to mitigate the negative impact of the correlation on the system performance. For the system with generalized fading modeled by eta-mu distribution and Cyclic Redundancy Check (CRC) Aided Successive Cancellation List (CA-SCL) decoding, the scenario with correlated fading channel and interleaving shows a performance improvement compared to the system without interleaving. In this case, a gain of approximately 3.5 dB is obtained considering a Bit Error Rate (BER) of 10^{-2}. Considering the alpha-mu (alpha=2 and mu=1) and the kappa-mu  (kappa=mu=2) fading channels,  the uncorrelated systems outperform the correlated ones. Among them, the interleaver improves the performance of the systems. For a BER of 10^{-2}, as an example, the use of fading correlated channels and interleaver shows a performance improvement of 12 dB and 0.5 dB for the alpha-mu and kappa-mu fading channels, respectively.