A cyclic redundancy check aided encoding construction method for list sphere polar decoder

Polar codes are the only error-correcting codes that have been mathematically proven to achieve the Shannon limit to date, playing a crucial role in the control channels of 5G mobile communication systems. For control channels, although the sphere decoding (SD) algorithm boasts excellent performance, its high computational complexity and significant latency present clear limitations in practical applications. In contrast, the list sphere decoding (LSD) algorithm strikes a balance between performance and complexity. This paper proposes a construction method that delays the decoding of specific information bits with the minimum row weight to mitigate the impact of error propagation. For scenarios where the total number of delay-decodable bits is limited, we introduce a segmented construction strategy. Through mathematical analysis, this strategy effectively increases the number of delay-decodable bits, thereby significantly reducing the impact of error propagation without changing the number of transmitted bits. Simulation results show that the decoding performance of the proposed algorithm is comparable to that of the SD algorithm at medium and low code rates (with a difference of less than 0.2 dB), but it abandons the concept of search radius in the SD algorithm and does not require a backtracking process. Furthermore, under high code rate conditions, such as P(32, 20), the proposed algorithm also maintains excellent performance.