## 4 Evaluation
### Evaluation for Compression Performance  
Next, we evaluate main three parameters that affect to the compression ratio: the number of bits of symbol, the one of the look-up table entries, and the hit counting for the entropy culling. Figure 7 shows the result when the symbol size of ASE coding varies between eight and 16 with comparing to the [PERSON]'s coding, LCA-DLT and deflate. The symbol size of ASE coding relates to the entropy of the original symbol, because the larger number of symbol bits has higher frequent probability. LCA-DLT and ASE coding work as stream-based and must process statistics by a limited size look-up table. Therefore, it is expected that the [PERSON]'s and deflate will show a better compression ratio than the ones of LCA-DLT and ASE coding. The graph shows that the compression ratio of ASE coding maintains 50-80%. Performance differences of the text-based cases between ASE coding and deflate are large. However, the ones of 4K images show small performance differences. This means that ASE coding effectively works for high entropy data. As a reference of buffered and complex compression method, deflate shows a much better compression ratio than ASE coding because it works as universal LZ-based compression with Huffman coding by creating a look-up table that can be dynamically extended. The Shannon's coding saturates the assigned code bits until the original symbol width. However, in the case of 16-bit width of Shannon's, the compression ratios become better than the eight-bit case, because the benchmark data do not have frequency of symbols less than \(2^{16}\). We can confirm that ASE coding compresses better than the Shannon's case, as we observed in the previous section. Figure 6: Comparison of compression ratios of ASE coding with varying the distance regarding the nearest neighbor entry exchange. Figure 7: Comparisons of compression ratios among ASE coding (8/16 bit symbol input) and the conventional methods. ASE coding maintains a better compression ratio when the symbol width is 16-bits. However, the benchmark of the MIDI pitch values shows worse. Therefore, we can understand that the symbol width is a sensitive parameter for ASE coding. However, we have a minimal guideline to decide the symbol width. The width should not be misaligned to the data generated from application. We recommend using a symbol width that is one or multiple times of the data width generated from the target application. In this evaluation, we confirmed that the guideline works well. Figure 8 shows the analysis when the number of look-up tables varies from four to 256. The DNA sequence is not affected by the number of entries, because the data consist of combinations of only four ASCII characters. This is caused by a reason why all ASCII characters of the sequence are cached in the table, even if the number of entries in the table is four. However, the entropy culling is working to remove those occupied entries. Although the entropy calculation generates always shorter mask bits, table hit ratio is not affected by the table size. Therefore, the compression ratios among different table sizes do not change in this experiment. On the other hand, the other cases show that all table entries are occupied. When the number of entries is too small, \(m\) from the entropy calculation becomes always \(M\). This finally degrades compression ratio. Although the compression ratio becomes better as the number of table entries is increased, it degrades again when the number of entries is too large. This means that we need to adjust the number of table entries, depending on entropy of streaming data. Figure 9 shows the analysis when the setting of the entropy culling is varied from two to 16 hits. When the culling frequency is too high (i.e., the counter is set to a small number), even though the compressed symbol becomes short, entries in the table are often invalidated. Besides when the culling frequency is low, the compressed symbol becomes larger. Thus, these cases cause bad compression ratios.