QR碼（quick response code）為一種使用里德-所羅門碼（Reed-Solomon code）編碼的二維條碼，但是QR碼視覺美感效果極低，因此有人採用以里德-所羅門碼的特性編出基線QR碼（baseline QR code），後續加上無失真標誌形成具有圖片視覺性的QR碼，稱為無失真標誌QR碼（lossless logo QR code）。此外，近幾年第五代行動通訊技術（5th generation mobile networks，簡稱5G）日漸普及下，在5G編碼中的極化碼（polar code）是許多人探討的錯誤更正碼（error correction code），本研究乃是使用極化碼解碼的特性改善無失真標誌QR碼的更正能力以及視覺性。
極化碼在進行解碼時，可以直接使用接收到訊號的機率資訊進行解碼，與里德-所羅門碼必須利用接收到的訊號先決定為何種位元在解碼的方式不同，前者稱為軟式決策（soft decision），後者稱為硬式決策（hard decision）。對於解碼端，軟式決策相較於硬式決策利用的資訊更多，所以軟式決策的錯誤更正能力較佳。
本文先進行基線QR碼編碼，為了保留基線QR碼的資訊，選擇系統性極化碼的編碼方法實現第二次的編碼，並將編碼出來的同位位元（parity bit）放置在不會影響圖片視覺的位置上，最後利用其擁有錯誤更正能力，用原始圖片遮掩會影響視覺上的資訊，將其稱為極化標誌QR碼（polar logo QR code）。此編碼可在有大量雜訊下，能正確解開資訊，同時擁有比無失真標誌QR碼更佳的視覺效果。

QR Codes are two-dimensional barcodes coded by Reed-Solomon codes. The visual effects of standard QR Codes are extremely low. Therefore, this thesis adopts the baseline QR code, which is coded by exploiting the characteristics of Reed-Solomon codes. It adds the lossless logo on the baseline QR code and is named lossless logo QR code. On the other hand, in recent years, 5G techniques are growing in popularity. Polar codes are a popular error correction code for 5G. In this thesis, the characteristics of polar decoding are used to improve the error correction capability and visual effects of lossless logo QR codes.
In polar decoding, the probability information of the received signals can be directly used for decoding. In contrast, Reed-Solomon codes need to decide the signal belongs to what bit (either 0 or 1). The former is called soft decision, and the latter is called hard decision. Soft decision utilizes more information than hard decision, so the error correction capability of soft decision is better than hard decision.
First, we encode the baseline QR code. To retain the information of the baseline QR code, the method of the second coding (i.e. polar coding) adopts the systematic form. The parity bits of systematic polar codes are put in places that will not affect the logo. Finally, we cover up the visual information with the original image. It is called the polar logo QR code. This proposed method can correctly decode the information in the presence of many noise types, and it has better visual effects than the lossless logo QR code.

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