近幾年來，由於極化碼(polar codes)和低密度奇偶檢查碼(LDPC)已經正式被納入5G的規格書中。因此極化碼得到了許多的討論，極化碼是一個被證明可以達到香農容量(Shannon capacity)當碼長(codelength)很長的時候。常見的解碼方式有順序消去列表法(SC)，但由於解碼的時候，先前判斷出來的結果會影響後來的輸出結果，因此整個解碼過程會發生極大的時間延遲，因此我根據學長先前的架構下去研究5G標準URLLC來改善解碼的速度並設法維持同樣的錯誤率，並且想辦法降低在解碼過程中程式的複雜度，過程中為了使底層的程式能夠運行得更快，我嘗試把組合語言的Matlab寫成C語言來加強運行速度。

在過程中我嘗試利用學長先前研究的SCL解碼架構，加入循環冗餘校驗（CRC）的檢核機制在這裡稱作CA-SCL，後來由於一開始的檢核機制是必須等整個流程都做完才能知道是否成功，因此我們嘗試把CRC分段在整個碼長中以下簡稱SCA-SCL，後來想降低程式運行的時間我們嘗試改變解碼時的樹狀圖，此解碼方式稱為適應性順序消去列表法(Adaptive SCL)好讓程式可以更快速的執行完畢，並且錯誤率不會高太多。

In recent years, due to the polarization code (polar codes) and low-density parity check code (LDPC) has officially been incorporated into the specification of the mobile broadband of 5G. Polar codes have received a lot of discussion, polar codes are proved to achieve Shannon capacity when the code length is very long. The conventional decoding of Polar codes is Successive-Cancellation (SC). However, while decoding, the previous decisions as input will decide the path for next decision, the entire decoding process will be leading to error propagation. The most important thing in communication is to pursue fast reception with low error rate. To reduce the latency, we find some ways to reduce the program complexity in decoding process. In order to make the program run faster, we tried to translate Matlab language into C language for decoding speed enhancement.

In the process, I try to take advantage of SCL decoding architecture, adding a cyclic redundancy check (CRC) referred to as CA-SCL. Later we try to segment the entire CRC code length referred to as SCA-SCL, then we try to change the tree diagram while decoding which is called adaptive Successive-Cancellation List (Adaptive SCL) for reducing the time of running the program, with not too high BLER.

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