On polarization adjusted convolutional codes over fading and additive white Gaussian noise channels

Ultra-reliable and low-latency communications (URLLC), which focuses on delay sensitive applications and services, is one of the three main pillars of 5G New Radio (NR) network architecture. URLLC's physical layer design is challenging since it must meet two contradictory requirements: ultra-low latency and ultra-high reliability. Short packets are used to minimize latency but at the cost of a significant loss of coding gain. Alternatively, system bandwidth can be increased, which is not always practical, particularly for some URLLC applications in industrial control that use unlicensed spectrum. In order to improve reliability, we must utilize robust channel codes in conjunction with retransmission techniques. Therefore, the construction of block codes with short blocklengths (e.g., a thousand or less information bits) is receiving significant attention with emerging wireless communications applications. In this thesis, we review existing channel coding bounds with short blocklengths for both additive white Gaussian noise (AWGN) and block fading channels. Furthermore, we investigate the performances of tail-biting convolutional, polar, and polarization adjusted convolutional (PAC) codes. With the motivation of reducing the decoding complexity of PAC decoders, we implement an alternative sequential decoding algorithm, namely, creeper algorithm, and describe a simplified list decoding approach. We also conduct an investigation on the performance of PAC codes and channel coding limits for block fading channels. Furthermore, we derive a method for computing approximate weight distribution of PAC codes, which can be used for an accurate performance bound; and, employing this approximation, we design PAC codes utilizing simulated annealing for optimization of the rate profiles. The results show that the newly designed PAC code rate profiles offer superior performance.