數位傳輸已經成為人類生活中不可或缺的部分，其中極化碼(polar codes)就是時下最熱門並且準備應用於第五代行動通訊(5G)的編碼方式。由於傳輸過程往往會因為受到各種干擾、雜訊影響等等因素導致接收到錯誤封包無法進行解碼。因此除了持續加強編碼技術降低錯誤率之外，發生傳輸錯誤後的重傳機制也成為了很重要的一環。
近年來，應用在極化碼的重傳機制上主要有兩種，分別是合併式自動重傳機制(CC-HARQ)以及冗餘式自動重傳機制(IR-HARQ)。前者的運作原理較為傳統，接收到重傳指令後重傳相同封包，然後在接收端整合兩次觀測結果並進行解碼；後者則是會根據極化碼固有的特性，重傳拓展碼長後的部分封包，之後再經由接收端將兩次觀測結果合併成新的極化碼，再進行解碼。
極化碼在經過重傳並且結合重傳的觀測結果之後，將會大幅降低錯誤率。本論文提出針對使用者所提出的碼長、碼率、通道環境等條件，利用兩項通訊傳輸上常見的指標，包括成功傳送的能量期望值(expected energy)以及吞吐量(throughput)，在固定傳送總能量下，調整前後傳送能量來估計出較好的整體傳送效果。
然而為了做分析而必須去做大量的模擬求得各種錯誤率，這件事本身是極度費時的，因此我們透過高斯近似的作法，快速的估測出有參考價值的不同條件下的錯誤率，來達到實用的最佳化估測。

With the advancement and convenience of technology, digital transmission has become an indispensable part of human life. Among them, polar code is the most popular one and ready to be applied to the fifth generation mobile communication (5G) coding. Because the transmission process is often influenced by various interferences, noise, and other factors, receiving an erroneous packet could lead the transmission failure. Therefore, in addition to continuously enhancing the coding technology to reduce the error rate, the retransmission mechanism in case of transmission error has become an important part.
There are two major types of retransmission mechanisms for polar codes, namely, the Chase Combined Hybrid Automatic Repeat reQuest (CC-HARQ) and Incremental Redundancy Hybrid Automatic Repeat reQuest (IR-HARQ). The former scheme operates in a conventional manner. That is, after receiving the retransmission command, the same packet is retransmitted, and then the observation result is integrated and decoded at the receiver. The latter scheme retransmits part of the extended code word. After the packet is retransmitted, the two observations are merged into the extended polar code, and then decoded.
Retransmission will greatly reduce the error rate. Considering the conditions of code length, code rate, and channel environment, this work proposes energy allocation among transmission and retransmission. The goal is to minimizing an indicator that consider the expected energy consumption and the expected throughput. However, in order to do the consumption for the energy allocation, it is necessary to do a lot of simulations to obtain various error rates. This is extremely time-consuming.
Therefore, we use Gaussian approximation to quickly estimate the value of reference under different conditions. The error rate thus obtained is then used to achieve a fast optimization for energy allocation.

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