High‐parity vertical Reed‐Solomon codes for long GNSS high‐accuracy messages

This paper presents in detail an outer-coding proposal for long GNSS messages disseminated by multiple satellites. The proposal minimizes the message reception time, or Time To Retrieve Data (TTRD), over a page erasure channel in most types of environments and visibility conditions. A message M consisting of k pages is encoded into a set C consisting of n pages, such that when any subset C′ of C of k pages is correctly received, the message can be decoded. The scheme vertically encodes each page symbol in a separate high-parity Reed-Solomon code and allocates different parts of it to different satellites. The scheme has been designed for the Galileo High Accuracy Service (HAS), but it can be used for longer messages and other constellations. The performance results show TTRDs on the order of few seconds, at a very low decoding complexity for the receiver.