# Concatenated Coding for GNSS Signals in Urban Environments
## 1 Introduction  
GNSS message coding schemes play an integral role in navigation system design, because they can enhance the robustness of the navigation data and therefore improve the positioning accuracy [1]. Historically, GNSS signals were designed for open-air scenarios in which the propagation channel model can be assumed as an AWGN channel. Hence, typical channel codes such as the Hamming code, the Bose-Chaudhuri-Hocquenghem (BCH) code, and the convolutional code are employed in GNSS signals for data message error correction [2; 3; 4]. As the demand for GNSS in urban environments continues to grow, the error correction capability of the GNSS coding schemes in urban channels has to be increased [5; 6; 7]. As a result, advanced channel codes are being introduced to modernized GNSS messages [8; 9; 10]. For example, LDPC codes are applied in GPS CNAV-2 messages [11], and non-binary LDPC codes are adopted in BDS-3 B-CNAV1 messages to achieve better performance than their binary counterparts [12]. However, the performance of the powerful LDPC codes dedicated to an AWGN channel is still limited in urban channels, and the high decoding complexity of the non-binary LDPC codes remains to be addressed [13]. Therefore, GNSS message coding schemes with better trade-off between error correction performance and decoding complexity are required to match the characteristics of urban channels. The concatenation of a binary inner code with a non-binary outer code,which leads to a more robust code to correct burst errors induced by fading channels, is a well-known process and is widely used in satellite communication systems [14]. For instance, a concatenation of an Reed-Solomon (RS) code and a rate-1/2 convolutional code (CC), called RS-CC concatenation hereafter, is recommended by the Consultative Committee for Space Data Systems (CCSDS) as a standard for telemetry channel coding. Concatenation schemes involving BCH codes, LDPC codes, Turbo codes, and polar codes are also implemented as the component codes [15; 16; 17]. Recently, several concatenation coding schemes have been introduced to GNSS messages. For example, the RS, LDPC, and lowest-density maximum-distance separable (LDMDS) codes are added as the outer codes to the rate-1/2 convolutional code for the optimization of Galileo I/NAV messages [18; 19]. Compared with the current I/NAV messages, these concatenated coding structures provide improvement of decoding performance under degraded channel conditions, as well as a reduction in the time-to-first-fix (TTFF). Moreover, other coding schemes to address struggling urban environments, along with the reduction in the TTFF, have been proposed for GNSS messages [20]. The purpose of this study was to investigate the use of concatenated codes as a good alternative to non-binary LDPC code for GNSS application in urban environments with relatively lower computational complexity and negligible degradation in decoding performance. Specifically, a serially concatenated coding scheme employing an RS outer code and an LDPC inner code, called RS-LDPC concatenation hereafter, is proposed to correct both random errors and burst errors, and hence, to improve the reliability of GNSS messages in urban environments. In particular, a two-state LMS channel was used to model the propagation properties of urban environments between the satellite and mobile terminals because of the low complexity and the good fitting effect [21]. Although RS-LDPC concatenation has been considered in some previous works [22; 23; 24], a detailed performance analysis targeted at GNSS messages over an urban channel has not been provided. The results of the comparison among various channel codes in this work could offer some useful indications for the optimization of GNSS message design.