Joint Design of Error Correction and Error Detection using CRC-aided Polar Code for Ultra-Reliable Space Communications and Navigation with Applications to GNSS L1C

This work investigates a concatenation of an outer CRC and an inner CRC-aided polar code to achieve ultra-reliable error performances for space and satellite communications with a direct application to GNSS L1C. By exploiting a unique feature of a CRC-aided polar code that exhibits an inherent trade-off between error correction and detection, we develop a joint design criterion to maximize the probability that the inner CRC can detect erroneous codewords that the outer CRC fails to detect. Different from traditional coding methods in space and satellite communications that treat error detection and error correction separately, the new design criterion helps us choose suitable inner CRCs of a given length to minimize the overall probability of undetected error (PUE) while maintaining a certain frame-error-rate (FER) level. Furthermore, by following the proposed design criterion, the overall PUE can be accurately estimated from the PUE of the inner code and the length of the outer CRC without the need for lengthy Monte Carlo simulations. The benefits of the new design are thoroughly demonstrated through PUE and FER performances of GNSS L1C Subframe 3. Specifically, by comparing the proposed concatenation of the 24-CRC with an inner CRC-aided polar code and the combined 24-CRC with the LDPC coded system currently used in GNSS Subframe 3, we observe that significant coding gains ranging from 0.6 dB to 1.1 dB can be achieved at a similar computational complexity.