## 2 Related Work  
The BeiDou-3 navigation satellite system's global short message communication service is integral to numerous monitoring systems operating where ground-based communication systems are unavailable [10; 11; 12; 13]. However, prevalent encoding formats within these systems often lack significant compression effects or prove unsuitable for our specific challenge. Traditional methods usually use related techniques of signal processing [11; 13]. In recent years, many studies have used machine learning for data compression [14]. Compression algorithms combined with machine learning are mainly used for images, sound and video, and text [15; 16; 17; 18], and machine learning is rarely used in the compression of instrument status data. Common compression algorithms applied to numerical data, such as vector quantization [19] and transformation coding [20], fail to ensure our fixed precision goals while maintaining high compression rates.  
Predictive coding presents the potential to achieve both objectives. Crucial to ensuring fixed precision is the encoding of residuals in predictive coding. The approach proposed by [PERSON] et al. [21] involves reducing the value range of residuals, while another approach proposed by [PERSON] and [PERSON] [22] adopts a variable precision floating-point format for encoding residuals, reducing precision for larger absolute values. However, both of them neglected meeting fixed precision goals, while neither approach guarantees fixed precision, especially considering sharp changes in ship states during engine start/stop cycles, rendering these methods unsuitable.  
The utilization of machine learning-based prediction in predictive coding holds promise for enhancing the precision of predicted values. Past research in the compression of text or genome data has demonstrated successful applications of predictive coding. For example, [PERSON] et al. [23] and [PERSON] [18] approached data as symbol sequences, employing prediction methodologies across the spectrum of potential data values. However, our scenario involving ship status data predominantly comprises floating-point data spanning an extensive range of potential values. This broad spectrum renders predicting every possible value's probability nearly unattainable, a challenge not present in the more confined scope of letters or genomes. Consequently, the application of their compression methodologies to our scenario is unfeasible. [PERSON] [13] proposed a data compression method specifically tailored for enabling communication through [PERSON]'s short message system. This method combines the Spinning Door Transformation algorithm for initial lossy compression and the Pre-special byte method for subsequent lossless compression. Nevertheless, this compression methodology is optimized for scalar sequences and cannot be readily adapted and optimized for our specific ship-status data structure, which consists of vector sequential data.  
The state-of-the-art data compression techniques available are primarily designed for general or specific scenarios that diverge significantly from the unique nature of our situation regarding real-time transmission of ship status data, particularly vector sequential data. Consequently, none of the existing methodologies can be directly applied to our context. This predicament underscores the necessity of devising a bespoke data compression methodology tailored explicitly to our specific scenario. This necessity has served as the driving force behind our research endeavors, which will be comprehensively expounded upon in the subsequent sections.