## 1 Introduction
In [19], a resource allocation scheme was proposed based on shipping lane information, which could improve the energy efficiency of the MCN. Despite these advancements, the development and optimization of channel coding techniques tailored for complex maritime environments remain a significantly understudied area in the literature. To fill this gap, we focus on a class of coding techniques designed to overcome challenges in maritime environments. Specifically, in our prior work [20], we investigated the performance of block Markov superposition transmission (BMST), a class of spatially coupled codes that convert short codes into codes with long constraint lengths through time-domain Markov superposition [21]. This architecture enables BMST to mitigate burst errors caused by maritime multipath propagation while maintaining high encoding efficiency. Our simulations validated its robustness in ship-to-shore communication scenarios. Beyond such point-to-point links, we further investigate the application of BMST in maritime two-way relay networks (TWRNs) [22, 23]. Such networks can provide beyond-line-of-sight (BLOS) connectivity for offshore terminals. However, conventional TWRNs enforce orthogonality by dividing the transmission resources (time/frequency) among users [24]. While orthogonal resource partitioning avoids interference, it inevitably results in spectral underutilization--a major bottleneck in maritime communication systems [25]. To concurrently address spectral efficiency, we employ physical-layer network coding (PNC), which converts symbol collisions into cooperative gains [26]. The synergistic integration of BMST and PNC provides a comprehensive solution that simultaneously tackles two critical challenges in maritime relay communications: (1) robust error correction against burst errors through BMST's spatially coupled architecture and (2) enhanced spectral efficiency via PNC's spatial-domain signal superposition. It should be noted that the initial simulations adopt an idealized assumption of equal path loss for both links in the TWRN, which simplifies the analysis but may underestimate performance variations in asymmetric channel conditions. In this manuscript, we consider a more realistic maritime relay communication scenario and propose a more flexible BMST-coded PNC scheme. Due to space limitations, we focus solely on the decoding algorithm design of PNC to further enhance reliability, while another issue in PNC, i.e., asynchrony, is left for future work. Specifically, our main contributions include the following three aspects:  
* We utilize log-normally distributed Rician factors to characterize maritime channel quality and rigorously evaluate the performance of the proposed scheme in TWRNs exhibiting asymmetric fading conditions across the two links. * We introduce a novel co-design framework based on BMST and PNC, achieving simultaneous improvements in both bit error rate (BER) performance and spectral efficiency. Furthermore, we incorporate a class of fixed-length multi-rate codes into the BMST-PNC system to address heterogeneous channel conditions while allocating code rates through channel capacity analysis. * We propose a novel iterative decoding and computing (DC) algorithm that sequentially executes iterative decoding prior to network coding operations. Benchmark evaluations demonstrate that the proposed DC algorithm achieves a 2.9 dB gain over a conventional computing and decoding (CD) algorithm at a BER of \(10^{-5}\). Furthermore, through targeted unilateral optimization, the DC algorithm attains an additional 0.2 dB coding gain under asymmetric fading conditions, demonstrating remarkable robustness across heterogeneous channel environments. The manuscript structure is as follows: Section 2 describes the system model and the maritime channel characteristics. Section 3 presents the encoding process and the DC algorithm for the BMST-coded PNC scheme. Section 4 provides a comprehensive analysis of the simulation results. Section 5 serves to conclude this manuscript.