隨著通訊技術發展，第三代合作夥伴計劃3GPP NR 裡提到第五
代通訊技術的規格中，因為極化碼具有很好的效能，所以被第五代通
訊技術採用。極化碼雖然在區塊錯誤率很低，但是極化碼有項先天上
的限制，那就是其碼長只能夠是2 的冪次方數，導致在各項應用上存
在很大的不便。為了能夠讓極化碼的碼長能夠任意選擇，第五代行動
通訊規格也提出了碼率匹配這項機制，能夠選擇要傳送的碼長。碼率
匹配有三種方式，分別是穿孔，縮短，以及重複。
在本篇論文中，我們只會去探討如何針對現有第五代通訊技術碼
率匹配中的穿孔和縮短這兩項機制，做改善和優化。穿孔這項機制的
運作方式為在編好極化碼之後，選擇不去傳送某些位元，如此一來就
能夠達到減短碼長的效果。縮短這項機制跟穿孔同樣也能達到減短碼
長的效果，但是和穿孔不同的地方是，穿孔在接收端並不知道不傳送
的位元，縮短則是知道不傳送的位元為何。重複這項機制，可以達到
延長碼長，方法是重覆傳送碼的某些位元。
我們提出的方法其原理為參考極化碼高斯近似法的子通道可
靠度排序和5G circular buffer 的順序，可以使得穿孔和縮短的區塊錯
誤率效能高於5G 的碼率匹配。

With the development of communication technology, 3GPP NR
standards discussions for 5G, polar codes have been adopted as the control
channel coding because of its good performance. Although the polar code
has the advantage of low block error rates, it has the disadvantage that its
code length can only be limited to a power of two, resulting in a large
limitation in various applications. In order to be able to choose the code
length of the polar code, the fifth-generation mobile communication
specification also proposes a rate matching mechanism, which can select
the code length to transmit. There are three ways to rate matching, namely
puncturing, shortening, and repetition.
In this paper, we will only discuss how to improve the two mechanisms
of puncturing and shortening in the existing 5G rate matching. The
puncturing mechanism works by selecting not to transfer certain bits after
coding, so that the effect of decreasing the code length is achieved.
Shortening is also achieves the effect of decreasing the code length. The
difference between puncturing and shortening is that the values of
punctured bits are unknown to the receiver and the values of shortened bits
are known in advance. The repetition mechanism works by selecting to
retransfer certain bits after coding, so that the effect of extending the code
length is achieved.
The method we propose is based on the sub-channel reliability
estimation by GA(Gaussian Approximation) and the 5G rate matching
circular buffer. It turns out that our method achieves a better BLER.

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