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.
Highlights
R ECENT years have seen a fast growing demand of mobile services with greater expectations for Quality of Service (QoS), ultra-low latency and high reliability standards. These requirements motivated the development of the 5th Generation (5G) of mobile communication systems [1]
It is important to mention that, according to the Technical Specification TS 38.212 Version 15.2.0 Release 15 produced by the ETSI 3rd Generation Partnership Project (3GPP) [22], a generator polynomial for the Cyclic Redundancy Check (CRC) of order r = 11 should be used for messages with length greater than or equal to 20 for the Uplink Control Information (UCI) encoded by polar codes
The use of the interleaver enhances the system performance from the correlated fading case in the direction of the uncorrelated case. This happens because burst transmission errors can degrade the system performance and interleaving shuffles the transmitted sequences improving the performance in terms of error detection and correction
Summary
R ECENT years have seen a fast growing demand of mobile services with greater expectations for Quality of Service (QoS), ultra-low latency and high reliability standards. Polar codes use the channel polarization technique to obtain almost noise-free channels that are suitable for transmission [9]. These codes, are theoretically significant because they achieve the symmetric capacity for binary discrete memoryless channels (B-DMC). The most suitable channels are chosen for the transmission of information bits, while the inputs to “bad” bit-channels are fixed to zero, known by both transmitter and receiver. The use of polar codes is extended from the AWGN channel in the direction of generalized fading channels modeled with α-μ [23], κ-μ [24] and η-μ [25] distributions.
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