Overview of various methods for decoding and constructing critical sets of polar codes

Polar codes have gained significant attention in recent years as they offer a promising solution for reliable communication in the presence of channel noise. However, decoding these codes remains a critical challenge, particularly for practical implementations. Traditional decoding methods such as belief propagation and successive cancellation suffer from complexity and performance issues. To address these challenges, authors have researched several low-complexity decoding techniques, including bit-flipping decoding with critical set construction. Bitflipping decoding methods operate by flipping a limited number of bits in the received codeword to bring the decoder output closer to the transmitted message. The critical set construction is an essential component of these methods, which identifies the set of bits to be flipped. This paper compares various bit-flipping decoding methods with different critical set constructions, including revised critical set, subblocks-based critical set, key set and others. The performance of these methods is evaluated in terms of bit error rate, computational complexity, and an average number of operations. In summary, this paper provides a comprehensive overview of bit-flipping decoding methods with critical set construction for polar codes. The paper's findings highlight the potential of these methods to improve the performance and reliability of polar codes, making them a viable option for practical implementation in modern communication systems.