Polar Code Encoding and Decoding Algorithms

In this article, we provide a comprehensive discussion of polar code encoding and decoding algorithms. Polar codes represent a cutting-edge coding technique with exceptional performance characteristics, widely adopted in modern communication systems. The encoding implementation involves transforming original data into polar code sequences through a recursive channel combining process, typically implemented using a generator matrix construction with Kronecker products. The decoding component employs the Successive Cancellation List (SCL) algorithm, which maintains multiple candidate paths during the decoding process to enhance error correction capability. The SCL algorithm achieves an optimal balance between decoding performance and computational complexity by keeping a fixed list size of most likely codeword candidates, significantly improving decoding accuracy compared to basic successive cancellation decoding. By integrating the SCL algorithm with polar code decoding, we enable reliable information transmission and reception with near-capacity performance. The implementation typically involves recursive probability calculations and path metric updates using log-likelihood ratios (LLRs). Therefore, polar code encoding and decoding algorithms play a crucial role in the design and implementation of contemporary communication systems, particularly in 5G standards for control channel coding.