極化碼的概念是由Arikan這位作者提出的，他證明極化碼是一種可以達到通道容量的編碼，當極化碼的碼長越長時，極化現象會變明顯，在長度趨近於無限大時會達到Shannon limits。為了增加短極化碼的極化效果，我們使用空間交錯的方法，來得到更好的效能，達到較低的錯誤機率。在這篇論文中我們採用兩種空間交錯的方法，第一種是編碼前輸入端的位元其位置交錯方法，而第二種空間交錯方法為編碼後輸出端的位元其位置交錯方法，這兩種空間位置交錯方法在不同的通道下會呈現不同的改善效果。

Proposed by Arikan, it was shown that polar codes are capacity-achieving codes. When the code length of a polar code increases, the channel polarization also increases. Moreover when the code length approaches infinite, the code performance achieves the Shannon limit. In order to enhance the channel polarization of short code, the spatial coupling methods are proposed in this thesis. The first method is the interlacing of input bits, and the second method is the interlacing of output bits. Simulation results show the pros and cons of two interlacing methods for different types of channels.

Abstract.......................I
摘要...........................I
第一章緒論.....................1
第二章極化碼的回顧.............3
第三章空間交錯方法............21
第四章總結....................45
附錄..........................46
參考文獻......................49

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