目前通訊技術的發展核心為無線通訊，由於極化碼具有很好的效能，且是第一種能在理論上被證明能達到通道容量的錯誤更正碼，因此後來也被第五代通訊技術(5G)採用，並做為控制通道的錯誤更正碼；但是在其規格中通道排序的部分，為了實務上的簡便，並沒有特別針對無線通訊中的環境來進行設計，所以將其用在無線通訊上會造成效能大幅降低，尤其是在高訊雜比區域，因此存在很大的改進空間。

另外在極化碼中，順續消去法(SC)會受到錯誤傳遞的影響，而為了改善此一現象，順續消去列表法(SCL)就被提出，其中在解碼過程分裂了多條路徑，能夠使其效能大幅提升，但也增加了整體的解碼複雜度。

因此本文首先針對瑞利快速衰落通道進行通道排序，並藉由通道排序所獲得的參數，進一步改善CRC 輔助順續消去列表法(CA-SCL)，提出一種減少路徑分裂的方法，稱之為分裂修剪CRC順續消去列表法(SR-CA-SCL)，經過模擬驗證後，在高訊雜比的環境中，能夠大幅降低CA-SCL解碼複雜度，且維持接近相等的錯誤率，使其在整體表現上能夠比CRC 輔助順續消去列表法(CA-SCL)更有優勢。

The core of current communication technology development is wireless communication. Polar codes, due to their excellent performance and being the first error correction codes theoretically proven to achieve channel capacity, have been adopted in the fifth-generation communication technology (5G) as the error correction codes for control channels. However, in the specifications of polar codes, the channel sorting aspect was not specifically designed for wireless communication environments for practical simplicity. Consequently, using them in wireless communication can lead to a significant decrease in performance, especially in high signal-to-noise ratio regions, indicating a great potential for improvement.

Additionally, in polar codes, successive cancellation (SC) decoding is affected by error propagation. To address this issue, successive cancellation list (SCL) decoding was proposed, which splits multiple paths during the decoding process to greatly enhance performance but also increases the overall decoding complexity.

Therefore, in this paper, we first perform channel sorting for Rayleigh fast-fading channels and then utilize the obtained parameters to further improve CRC-assisted successive cancellation list (CA-SCL) decoding. A method called Split-Reduced CRC-Aided Successive Cancellation List (SR-CA-SCL) is proposed, which reduces path splitting. After simulation verification, it has been demonstrated that SR-CA-SCL can significantly reduce the decoding complexity of CA-SCL while maintaining a comparable error rate, particularly in high signal-to-noise ratio environments. This approach exhibits superior overall performance compared to CRC-assisted successive cancellation list (CA-SCL).

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