近年來，無線通訊越來越發達，第五代行動通訊(5G)技術備受矚目。在5G規格中，極化碼被選為其中一種錯誤更正碼的編碼方案。極化碼的特性是不停地將好通道及壞通道兩極化，只要極化碼的碼長越長，極化效果越明顯，錯誤率越低。
當訊息傳送時，往往會受到各種干擾因素或是雜訊影響，使接收端解碼失敗，其中有一種改良的做法，是在解碼失敗後要求傳送端重新傳送，稱之為重傳機制。在5G的規格中，應用在極化碼的重傳機制有兩種，分別是合併式自動重傳機制(CC-HARQ)及冗餘式自動重傳機制(IR-HARQ)。
在無線傳輸中，使用的通道背景在數學上時常被模式化為衰落通道，其中又以瑞利衰落通道最為常見。本論文利用數學推導的方式，分析極化碼在瑞利衰落通道中的錯誤率表現。首先，推導衰落通道的錯誤率估計，接著分析分集技術的錯誤率估計法，最後整理出，在CC-HARQ機制下，錯誤率估計的流程。在估計CC-HARQ的錯誤率過程中，可以得到一些相關的數據，包含平均傳輸能量以及傳輸延遲等等。利用這些數據，我們可以快速算出將傳輸能量及傳輸延遲等因素綜合考慮所得之代價 (可以指定不同因素之間的相對權重)，並據以調整系統運作時之相關參數(例如：初始傳輸及重傳等各個不同階段所使用之能量)，使得整體代價可以達到最小化。

In recent years, wireless communication is more and more developed, and the fifth generation of mobile network (5G) technology has attracted much attention. Polar codes are selected as one of the channel coding techniques for 5G. The characteristics of polar codes is that the good channel and the bad channel are polarized continuously. The longer the code length is, the more obvious the polarization effect is, and the lower the block error rate (BLER) can be obtained.
When a message is transmitted, the receiver often fails to decode due to the effects of various interferences and noise. One of the ways to solve this problem is to request the transmitter to retransmit if the decoding fails, called retransmission mechanisms. There are two retransmission mechanisms as specified in the 5G standards, namely, the chase combined hybrid automatic repeat request (CC-HARQ) and the incremental redundancy hybrid automatic repeat request (IR-HARQ). In this thesis, the polar coding incorporated with CC-HARQ over fading channels is investigated.
In wireless transmission, the channel background used is often mathematically modelled as a fading channel, where in the most common is Rayleigh fading. This thesis uses mathematical derivation to analyze the BLER of polar codes over the Rayleigh fading channel. First, we derive the BLER estimation of a fading channel. Then, we analyze the BLER estimation using diversity combining. Lastly, we can derive the process of BLER estimation of CC-HARQ. During the process of estimating the BLER of CC-HARQ, we can obtain some relevant data including average power, delay, etc. Using this data, we can quickly obtain the cost considering transmission energy, delay and other factors (the weight between different factors can be specified), and use it to adjust the best parameters to be adopted by the system (for example: the energy used at different stages such as the initial stage and retransmission), so that the overall cost is minimized.

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