## 2 HAS Message Format and Decoding Performance Metrics  
The transmission of the HAS message features several layers of encoding that are implemented at both single signal and constellation levels. A summary of the different levels of encoding is provided in Figure 1[21]. Each E6B page lasts one second and is made of 1000 symbols with a 1 ksymbol/s data rate. The first 16 symbols of each page are not encoded and form the preamble used for page synchronization purposes. The remaining 984 symbols are Forward Error Correction (FEC) encoded with a convolutional code with rate \(1/2\). This type of encoding provides a first layer of protection against transmission errors which can be corrected using a Viterbi decoder. In the context of this paper, soft-decoding [4] is considered. In more detail, the navigation message is extracted from the prompt correlators that are obtained by integrating the received signal over 1 ms. Each E6B symbol is thus extracted from one correlator output. When hard-decoding is applied, a first decision (hard decision) is made and a binary value is extracted from the sign of each correlator output. These binary values are passed to the Viterbi decoder, which operates on hard values. In soft-decoding, the raw correlator outputs (soft values) are passed to the Viterbi decoder, which can achieve better performance. After Viterbi decoding, a set of 492 bits is found. The first 14 bits of the decoded message represent the E6B header. This field is currently reserved and can be used, for example, to discriminate valid pages from dummy messages. The subsequent 448 bits are the actual HAS page, which is then followed by the CRC (24 bits) and the tail (6 bits) used for completing the decoding the convolutionally encoded symbols. During the three months of data collection considered in this work, dummy E6B pages were broadcast. For this reason, the content of the transmitted pages was known at the receiver side; this fact was exploited to estimate the BER. The BER estimated using real E6B data was then compared to the theoretical one. It was expected that the E6B data is obtained using soft-decoding and in the presence of Gaussian noise. Figure 1: Different levels of encoding, error correction, and error detection implemented in the E6B HAS message transmission. The 24 bits of the CRC was used to detect if a page, after Viterbi decoding, was received without errors; only pages passing the CRC was used for recovering the final HAS message. In this paper, the CRC was used to evaluate the HAS page availability during the vessel trajectory. Specifically, the PER was computed as the ratio between the number of pages with passed CRC and the total number of received pages. Viterbi decoding and CRC verification are applied to each satellite signal individually, and are part of the single satellite level protection implemented to deliver correct HAS pages. This level of protection is complemented by a second layer implemented at the constellation level: each Galileo satellite transmits a different subset of HAS pages encoded using a Reed-Solomon approach [3; 21]. This approach allows one to reconstruct the original message with any subset of received pages of sufficient size. This mechanism is better detailed in [3] and allows the generation of a redundant set of \(N\) pages from an original message of \(K\) unencoded pages. Any subset of \(K\) different pages out of the \(N\) broadcast pages enables the reconstruction of the original HAS message. This property, along with an efficient page allocation scheme between the different satellites [6], allows a fast reconstruction of the HAS message. The TTRD, which is the time required to reconstruct the original HAS message, is an indicator of the capacity to timely provide high accuracy positioning. This metric was evaluated using the methodology discussed in [7; 8] where real data were used to simulate realistic transmission conditions. Moreover, the TTRD was determined adopting the dissemination scheme described in [7].