本論文提出二進制算術編碼法與基於上下文的二進制算術編碼法的解析解，因此，相對於傳統方法，所提出解析解的執行時間有明顯的改進。實驗結果顯示所提出的方法優於目前主流方法，如不用乘法的Q編碼（MQ編碼）與以基於上下文的自適應二進制算術編碼（CABAC）。實驗結果也顯示，在可接受的執行時間下，所提出二進制算術編碼法與基於上下文的二進制算術編碼法的解析解其壓縮率較MQ編碼佳。此外，透過所提出的解析解，原二進制算術編碼法與基於上下文的二進制算術編碼法的執行時間可以分別減少大約16%與27%。相較於原CABAC，在可接受的壓縮率下，所提出的二進制算術編碼法與基於上下文的二進制算術編碼法的執行時間可以分別減少大約73%與66%。所提出之解析解實質地改進了二進制算術編碼法與基於上下文的二進制算術編碼法的編碼速度。

In this thesis, analytic forms of binary arithmetic coding (BAC) and context-based binary arithmetic coding (CBAC) are proposed, with the aim of significantly improving their execution times compared with conventional approaches. The experimental results show that the performances of the proposed methods are comparable to those of state-of-the-art methods, such as the multiplier-free Q-coder (MQ-coding) and context-based adaptive binary arithmetic coding (CABAC). The experimental results also show that, under acceptable execution time, the compression ratios of the proposed analytic forms of BAC and CBAC demonstrate better performance than does MQ-coding. In addition, the execution times of conventional BAC and CBAC are reduced to approximately 16% and 27%, respectively, by the proposed analytic forms. Compared with CABAC, the proposed analytic forms provide a substantial improvement in coding speed, where the execution times are reduced to approximately 73% and 66%, respectively, by the proposed analytic forms of BAC and CBAC with an acceptable compression ratio.

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