Novel Shortened Polar Codes for GNSS L1C Subframes 2 and 3

This paper proposes promising CRC-aided shortened polar codes that can be used to replace the existing low-density-parity-check codes (LDPCs) in Global Navigation Satellite Systems (GNSSs) L1C Subframes 2 and 3. To achieve non-power-of-two frame lengths of 1, 200 and 548 coded bits in Subframes 2 and 3, respectively, we utilize detailed characterizations of the Kronecker construction of polar codes and propose a novel algorithm to identify 848 and 476 shortening positions from polar generator matrices G2048×2048 and G1024×1024. Different from the previously proposed shortening schemes, our method exploits a direct connection between the Hamming weights of columns of the polar mother code and the power-of-two decomposition of the number of shortening positions. For a given reliable sequence, the least reliable bit positions suitable for being shortened are generated by sequentially choosing relevant columns of G. Extensive simulations are then conducted to demonstrate the competitiveness of the proposed polar coding schemes over the current LDPC codes used in GNSS L1C. Specifically, it is shown that the proposed scheme provides significant coding gains, ranging from 0.35 dB to 0.55 dB, at the frame-error-rate (FER) level of 10?4 to 10?5 over GNSS LDPC codes in Subframes 2 and 3 at a comparable decoding complexity. These notable coding gains are achieved over both a static channel as well as a three-state fading channel, which accurately characterizes the significant dynamic fading effects observed in land mobile-satellite services (LMSS) expected in urban GNSS applications. The FER advantage of the proposed shortening scheme over the traditional shortening scheme adopted in 5G NR is also clearly demonstrated. With their large FER performance improvement, the proposed polar codes can therefore serve as an attractive alternative for the LDPC codes currently used in GNSS L1C protocols.