# Improving Data Communication of Enhanced Loran Systems Using 128-_ary_ Polar Codes
## 1 Introduction  
The enhanced Loran (eLoran) system has become a vital terrestrial backup for the Global Satellite Navigation System (GNSS), owing to its strong anti-jamming capabilities and improved operational stability [1, 2, 3, 4, 5]. A core function of eLoran is data communication, which traditionally consists of two main components: (1) 128-_ary_ Pulse Position Modulation (PPM), which is fundamental to the system's positioning capability, and (2) Reed-Solomon (RS) coding for data encoding [6]. Current research efforts to improve the error performance of eLoran data communication have primarily concentrated on refining modulation and demodulation techniques [7, 8, 9, 10]. However, such improvements in demodulation methods typically yield only incremental gains in error performance. On the other hand, any modification to the modulation scheme risks undermining the established positioning functionality, which is critical for eLoran's operational integrity. Therefore, enhancing the data encoding process emerges as a more promising and less disruptive approach to achieving significant improvements in error performance while maintaining full compatibility with the existing positioning infrastructure. The RS code, introduced by [PERSON] and [PERSON] in 1960 [11], is the conventional choice for eLoran data encoding. In practice, RS codes are predominantly decoded using hard-decision decoding (HDD) algorithms, such as the Berlekamp-Massey (BM) algorithm [12], the Euclidean algorithm [13], and the Welch-Berlekamp algorithm [14], with the BM algorithm being the most widely adopted for eLoran [6]. Theoretically, soft-decision decoding (SDD) offers superior error correction compared to HDD, with Maximum Likelihood (ML) decoding being optimal. But the ML decoding process for RS codes is known to be NP-hard [15], making it impractical for practical applications. And existing SDD algorithms for RS codes, such as the chase Kotter-Vardy algorithm [16], partially parallel low-complexity chase algorithm [17], and the Bit-level Generalized Minimum Distance (BGMD) algorithm [18], provide only limited performance gains at the cost of significantly increased complexity. This situation highlights the inherent limitations of RS codes in further improving the error performance of eLoran data communication. Given that eLoran data are transmitted in short-code, this paper proposes the adoption of polar codes, which are particularly well-suited for short-code applications. Polar codes, proposed by [PERSON] [19], are theoretically proven to achieve the capacity of arbitrary symmetric discrete memoryless channels (DMCs) and were adopted in the 5G mobile communication standard in 2016 [20]. The fundamental principle underlying polar codes is channel polarization, which transforms a set of identical binary-input DMCs into a series of polarized subchannels with widely varying channel error rates (CERs): some subchannels exhibit CERs approaching zero, while others approach one. Information is transmitted over the most reliable subchannels--those with CERs near zero. The classic SDD algorithm for polar codes is the Successive Cancellation (SC) decoder, also proposed by [PERSON] [19], which has a complexity of \(O(N\cdot log_{2}N)\), where \(N\) is the code length. In this work, we propose the adoption of a 128-_ary_ polar code specifically designed for the eLoran system, aiming to replace the conventional RS code while preserving the 128-_ary_ PPM. This ensures that the proposed enhancement does not compromise the system's core positioning function. Since the SC decoder for polar codes requires soft information as input, we introduce a Soft-Soft (SS) demodulation method based on a correlation receiver.