CRC-Aided Polar Code for GNSS L1C Subframes 2 and 3: Enhanced Information Set and Optimal CRC Selection

This work investigates an enhanced concatenation of an outer cyclic redundancy check (CRC) and an inner shortened polar code for GNSS L1C Subframes 2 and 3, aimed at improving frame error rate (FER) performance. The key contribution lies in the construction of a new information set that yields a shortened polar code with twice the minimum Hamming distance of the existing design. This information set is obtained by identifying rows of the information set that limit the minimum distance and replacing them with positions of higher reliability in the frozen set while preserving the underlying shortening pattern. Notably, the resulting code structure enables an explicit enumeration of minimum-weight codewords for any candidate CRC polynomial, allowing the selection of an optimal CRC-11 from the full set of 1,024 generator polynomials by directly minimizing the number of minimum-weight CRC-aided codewords, a metric tightly linked to FER performance under maximum-likelihood decoding. Simulation results for both subframes demonstrate clear FER gains over the GNSS LDPC codes specified in IS-GPS-800 as well as over previously proposed CRC-aided shortened polar codes. The findings indicate that the combination of the proposed information set and the optimized CRC provides a strong foundation for next-generation GNSS message design, supporting improved robustness and high-precision positioning.