Design and Analysis of Advanced Polar-Coded Communication Systems

Polar codes are a category of error-correcting codes which have excellent performance and have been used in the control channel in the fifth-generation (5G) communication systems standard. They are expected to also be used in the next-generation massive multiple-input multiple-output (MIMO) systems where sparse coding, low-complexity decoding and optimum resource allocation are the main focus. In this thesis, we have considered three main areas in the context of next-generation communication systems where the design and analysis of polar codes could enhance the system performance. These areas are: spatial modulation (SM) with multilevel coding (MLC), specifically, low complexity soft-cancellation (SCAN) decoding with deep neural network (DNN) assisted bit flipping, and reconfigurable intelligent surfaces (RIS) assisted wireless communications. This is the first work to apply multilevel polar code design to multiple-antenna index modulation schemes such as space-shift keying (SSK) and SM. First, we propose a multilevel polar code design for an SSK-modulated MIMO system. Polar codes have been shown to perform excellently when used with the MLC design paradigm, as the rate allocation of the component polar codes follows the natural polarization inherent in polar codes. We use the capacity rule to evaluate the bit-level ergodic capacities of SSK modulation. The proposed MLC-based polar-coded system outperforms the corresponding system that uses bit-interleaved polar-coded modulation. Next, we address the problem of low-complexity polar decoding for next-generation communication systems. Bit-flipping has recently been applied to the low-complexity SCAN decoder using a fixed list obtained from heuristic bit-flip probability data. This fixed bit-flip list may lead to bit-flip positions with a high probability of error incorrectly given a low flipping probability for a given received codeword. To mitigate this problem, we propose to use a DNN to identify the positions of flipped bits in the soft output of the SCAN decoder that are incorrectly classified for the additive white Gaussian noise (AWGN) channel. Finally, we propose a semi-analytical method to design polar codes for the RIS-assisted channel with Rayleigh fading on each wireless link, while also providing an approximate closed-form expression for its word error rate (WEP) as a function of the number of RIS elements. We introduce an exponential approximation to determine closed-form expressions of the bit-channel transition probabilities that are independent of the SNR and the number of RIS elements, which can be tracked throughout the design process. This allows the core design process to be independent of the SNR and the number of RIS elements, enabling rapid determination of the WEP for any combination of RIS elements and SNR. The proposed method accurately determines the number of RIS elements required to achieve a target WEP for a specific SNR and can be used to optimize resource allocation in multi-user scenarios, surpassing traditional exhaustive search methods.