傳統錯誤更正碼所對抗的通道錯誤是替代錯誤，並沒有考慮同步錯誤的情況。如果在一個會發生同步錯誤的通道上使用傳統錯誤更正碼，那麼一旦發生一次同步錯誤，在之後的所有碼字都會因為不對齊而造成錯誤。因此，針對同步錯誤通道設計特別的錯誤更正碼是必要的。最早是由Sellers開始注意到這個問題，他的做法是在每個碼字間插入特別的同步用序列。之後Levenstein發現原先由Varshamov，Tenegolts兩人所發明用來對抗Z通道的VT碼，也可以用來對抗同步錯誤，並進一步地推導出許多同步通道中重要的基本性質。他的做法是每一個固定長度的碼字，可以改固定個數個同步錯誤，後來的多數研究都是類似這種做法。唯一不同的是MacKay，他把低密度同位元檢查碼和一串稱為浮水印碼的序列做互斥運算，用浮水印碼抓回同步，再用低密度同位元檢查碼更正錯誤。

除了錯誤更正碼的設計，計算同步錯誤通道的通道容量也是一個一直存在的問題。由於同步錯誤通道並不具有無記憶性的特性，使得分析起來相當困難，除了數值逼近的方法外，直到現在都還只有通道容量的界限。

而本篇論文主要針對同步錯誤中的複製錯誤，基於前人把複製通道簡化成複製區塊通道的概念，分析複製區塊通道，進而設計適合的錯誤更正碼，以達到通道容量為目標。並分為零錯誤傳輸方式和允許錯誤傳輸方式兩方面來討論。

Insertion and deletion errors are two main classes of synchronization errors.
In this thesis, we focus on duplication errors, which is a subclass of insertion errors.
Our aim is to find error correcting codes for duplication channels which have a code rate per unit cost higher than 0.5, a rate per unit cost of a simple zero-error coding scheme.

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