近年來隨著無線通訊系統的發展，在邁向5G移動通訊的時代裡，使用了一種編碼方式，稱作極化碼(Polar Code)。極化碼則是在2009年由Arikan教授所提出的。Arikan教授所提出的極化碼裡面提到了一種解碼方式，稱為順續消除法解碼(Successive Cancellation，簡稱SC)，但是此解碼的效能與方式不近理想，而後來則發展出順續消除列表法解碼(Successive Cancellation List，簡稱SCL)，置信傳播法解碼(Belief Propagation，簡稱BP)，軟消除(Soft Cancellation，簡稱SCAN)之類的更有效，更方便實施在硬體上的解碼方式。
軟消除解碼(SCAN)是基於順續消除解碼(SC)與置信傳播解碼(BP)的結合，此解碼方式不但擁有了優化效能且方便應用在硬體上的優勢，在現今極化碼的估計方法上有了高斯近似法(Gaussian Approximation，簡稱GA)，可以來估計部分解碼方式的錯誤率。
此論文研究方向會在軟消除解碼(SCAN)與高斯近似法 (GA)上的結合去作研究。由於極化碼正常模擬下花費的時間太過冗長，所以會導致使用者無法快速地得到所需的訊息。目前利用高斯近似法(GA)的演算法，來估計出軟消除解碼(SCAN)的錯誤率，稱作軟消除估計法(SCAN Estimation)，來節省極化碼在正常模擬下所多花費的時間。
另一方面，此論文也針對軟消除估計法來提出一種獲得最佳化問題的分配，並且使用夾擠法(Squeezing Method)來加速分析。

In recent years, with the development of wireless communication systems, in the era of 5G mobile communication. An encoding method has been used, which is called polar code. The polar code was proposed by Professor Arikan in 2009. He mentioned a decoding method called successive cancellation decoding (SC), but the efficiency and method of this decoding are not ideal so later some researches developed the successive cancellation list decoding (SCL), belief propagation decoding(BP), soft cancellation(SCAN), refer to more effective and easier to implement.

Soft cancellation decoding is based on the combination of successive cancellation decoding and belief propagation decoding, SCAN decoding method not only has the advantages of improved performance and easy implementation on hardware. There is a Gaussian Approximation (GA) in the current estimation method of polarization codes, which can estimate the error rate of some decoding methods.

The research direction of this paper will be on the combination of soft cancellation decoding and Gaussian approximation. Since the time spent in the normal simulation of the polar code is too long, it will cause the user to not get the required information quickly. At present, the algorithm of Gaussian approximation is used to estimate the error rate of soft cancellation decoding, which is called SCAN estimation, to save the time spent by polar codes under normal simulation.

On the other hand, as an application of the SCAN estimation, this paper also proposes a setting to obtain the optimization problem for the soft cancellation estimation method, and uses the squeezing method to speed up the computation.

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