一種編碼如果同時是前綴碼(prefix code)與後綴碼(suffix code)，則稱這一種編碼為fix-free碼。對於一個使用fix-free碼編碼的資料， 可以同時由收到資料的前端與後端同時解碼，因此可以加快解碼的速度。如果當資料由前端開始解碼且在收到的資料中有錯誤發生，則可以由後端繼續解碼因而復原發生錯誤之位置後面的資料。目前關於fix-free碼的研究方向大約包含︰討論fix-free碼存在的充分必要條件和建構方法、如何有效的編碼、對於編碼資料發生錯誤下的解碼或同步問題、如何應用fix-free碼於實際上，例如fix-free碼已經被發展應用於H.263+與MPEG-4等影像標準上面。本篇論文著重於討論fix-free碼存在的充分條件與建構方法。

雖然fix-free碼同時是前綴碼與後綴碼，但其結構卻遠比後兩者複雜。到目前為止還未有一個定理可以完整地判斷給定的字碼長度是否存在fix-free碼，且建構其對應的fix-free碼。Ahlswede等人推測一個fix-free碼存在的充分條件為: 如果字碼長度滿足
$$\sum_{l \in L} 2^{-l} \leq \frac{3}{4}$$
則會存在fix-free碼，其中L是所有字碼長度所形成的集合。目前為止只有在某些特殊條件下這一個推測才成立，且沒有反例可以推翻這一個推測。本篇論文裡，我們證明一個fix-free碼存在的充分條件: 如果字碼的長度只有4、6或8，且長度為4的個數少於或等於4個，長度為6的少於或等於8個，且如果字碼長度的Kraft sum小於或等於3/4，則存在一組fix-free碼。最後我們提供了由已知的fix-free碼來建構另一組fix-free碼，以及由兩組已知的前綴碼與後綴碼來建構fix-free碼的方法。

A code is a fix-free code if it is both a prefix code and a suffix code. Data encoded by a fix-free code can be decoded in the forward direction and the backward direction simultaneously, thus reducing the decoding time by half. In this thesis, we prove a sufficient condition for the existence of fix-free codes and provide some methods to construct a fix-free code from existing codes.

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