## 4 Experiments and Results
### Experimental Setting
#### 4.1.3 Experimental Design  
Our primary objective in the ship status data transmission scenario is to compress real-time data approaching its theoretical minimal length, enabling real-time transmission via the Beidou navigation system. Our optimization focus lies in achieving a long-term average compression rate for compression algorithms, reflected in the average code length post-compression. Given the steps involved in these algorithms--initially estimating symbol occurrence probabilities followed by arithmetic coding--the average code length closely aligns with the information entropy value calculated from these probabilities.  
In our approach, we estimate the summed code length of encoding methods using the information entropy of estimated probabilities. This estimation enables us to gauge the compression rate of different algorithms. Sequential information entropy is estimated using commercial compression software, calculated as the compressed file size divided by the number of data points. Notably, the minimum achieved result across various configurations of compression software stands at 141 bit.  
We devised a series of experiments to assess the effectiveness and reliability of our designed compression algorithm for real-time ship status data:  
* **Experiments to estimate data frequency estimation effectiveness:** We evaluated the validity of the frequency estimation method employed in our study for future data. This analysis involved learning curves and performance comparison on training and validation sets. Estimation used the early part of the training data to gauge frequency and calculate information entropy.
* **Ablation Experiments on our compression algorithm (QAAPA):** We conducted experiments to analyze the key steps in our QAAPA method--Quantization, Attention-Averaging-based Predictive Coding, and Arithmetic Coding. We trained the attention averaging-based predictor by initially training the linear and CNN models separately. The subsequent training of the attention averaging model involved freezing linear model parameters for 20 epochs and using a constant learning rate of 5e-4. We implemented models in Keras with TensorFlow as the backend, trained on an Nvidia Quadro K620 GPU. We compared the summed coding length before and after applyingour QAAPA method across training, validation, and test datasets. Additionally, we assessed individual steps within QAAPA by comparing it with alternative methods:  
* Original: only encoding data in _float64_ format without data compression
* Q Method: Solely employing Quantization for data compression.
* QA method: Employing Quantization and Arithmetic Coding for data compression. All of the above methods remove one or more steps from our QAAPA method. The following two methods replace the averaging-attention-based predictor of our QAAPA method:
* QLRPA: Replacing the attention-averaging-based predictor in QAAPA with linear-regression-based predictive coding and including Quantization, linear-regression-based predictive coding, and Arithmetic coding for data compression.
* QCNNPA: Replacing the attention-averaging-based predictor in QAAPA with CNN-based predictive coding and including Quantization, CNN-based Predictive coding, and Arithmetic coding for data compression.
* **Experiments on the reliability of our QAAPA method:** This experiment involved comparing compression results using our QAAPA method across training, validation, and test sets. The compression results are evaluated by the following descriptive statistics, including the mean value, standard deviation, minimum value, 25 th percentile, median (50 th percentile), 75 th percentile, and maximum value. In addition, we analyzed the transmitted code length via Beidou over time to evaluate the reliability of our method.