傳統上，我們通常使用訊號源符號機率對其字碼長度之加權平均值來做為衡量對訊號源編碼效率的評估標準，但在某些通訊環境下，此種評估標準無法適當並正確地反應出對訊號源編碼所實際付出的代價。
有別於傳統上所習慣採用的平均長度，在此篇論文中，我們採用由Campbell 在1965年所提出的指數加權平均長度來衡量編碼之率，其假定對訊號源編碼所付出的代價與字碼長度成一指數關係，並且可將其視為傳統平均長度之推廣。在若干通訊的傳輸環境之下，採用 Campbell 所提出的平均長度來評估編碼之效率較使用傳統的平均長度更為適當，特別是在編碼和解碼所需之成本很高或是過長的字碼會造成儲存元件之暫存區滿溢並導致資料流失。
在採用 Campbell 所提出的平均長度來做為衡量對訊號源編碼效率之標準的前提下，於本篇論文中，我們推導一些最佳二位元前綴碼(prefix code)之性質，並且在訊號源符號機率分佈之部分資訊已知的情況下－特別是在任意多個訊號源符號之機率、訊號源符號之最大機率或是最小機率已知的情形下，我們分別探討並提供若干最佳二位元前綴碼之 Campbell 平均長度的上界限與下界限。
本篇論文的主要貢獻在於除了可在實際通訊環境上提供比目前已知結果更精確的效能評估，亦可將其應用於訊息理論中之猜測與賭博問題的研究上。

In this thesis, we consider the exponentially weighted average codeword length introduced by Campbell as a performance measure for source codes. This criterion assumes that the cost is an exponential function of the codeword length and includes the usual expected codeword
length criterion as a special case. Such situations could arise when the cost for encoding and decoding is significant, or if the buffer overflow caused by long codewords is a serious issue. Under Campbell's average codeword length criterion, we derive new upper and lower
bounds on the exponentiated expected length of optimal binary prefix codes when partial information about the source symbol probabilities is available.

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