近年來QR碼已經被廣泛地使用在我們的日常生活中。對比於一般的一維條碼，QR碼的優點在於可以儲存更大量的訊息，且在掃描時也不必對準方向。但隨著應用越來越多元化，QR碼內建的RS錯誤更正碼並不能很有效地應付各種情況。我們在此提出了使用極化碼來輔助QR碼，改善QR碼的容錯能力。
極化碼是目前唯一一個可以被嚴格證明達到通道容量的編碼方式，因為其優異的錯誤更正能力，才選擇使用它來加強QR碼。我們的做法是將標準的QR碼拿去做系統性極化編碼，編碼後會產生多的校驗碼，再將影像改為四種亮度來放置這些校驗碼。為了不影響標準QR碼的架構，我們將四種亮度區分為MSB和LSB兩層，其中MSB的部份不改變，而將系統性極化碼的校驗碼放在LSB的部分，形成一個不影響標準架構的兩層強化型QR碼。
最後比較各種不同的情況，可以發現在解碼成功率方面都比標準的QR碼表現來得更加優異。

In recent years, QR codes have been used in daily lives widely. In contrast with one-dimension barcodes, the advantage of QR codes is that they can store a large amount of information, and they don’t have to be carefully aligned when they are scanned. However, as the application becomes more diversified, the RS error correction code, which is built in QR codes cannot deal with various situations effectively. In this work, we propose to use polar codes to assist QR codes for improving their error correction capability.

Polar codes is the only channel coding technique that can be mathematically proved to achieve channel capacity. In this work, it is chosen to enhance QR codes because of its excellent error correction capability. Our approach is to feed the standard QR codes into systematic polar encoding, and then change the two-brightnesses QR image into four-brightnesses for accommodating the extra parity bits produced by the polar encoding. We divide four-grayscale module into MSB and LSB in order not to change the construction of standard QR codes. More specifically speaking, the original QR-code data bits are placed in the MSB layer. Finally, we place the parity part in the LSB layer.

We test this enhanced QR codes in many different situations by simulation, it is found that the decoding success rate is superior to the standard QR codes.

1. Reed, I. and G. Solomon, Polynomial Codes Over Certain Finite Fields. Journal of the Society for Industrial and Applied Mathematics, 1960. 8(2): p. 300-304.
2. Arikan, E., Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels. IEEE Transactions on Information Theory, 2009. 55(7): p. 3051-3073.
3. Mori, R. and T. Tanaka, Performance of polar codes with the construction using density evolution. IEEE Communications Letters, 2009. 13(7): p. 519-521.
4. Sae-Young, C., T.J. Richardson, and R.L. Urbanke, Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation. IEEE Transactions on Information Theory, 2001. 47(2): p. 657-670.
5. Trifonov, P., Efficient Design and Decoding of Polar Codes. IEEE Transactions on Communications, 2012. 60(11): p. 3221-3227.
6. Tal, I. and A. Vardy, List Decoding of Polar Codes. IEEE Transactions on Information Theory, 2015. 61(5): p. 2213-2226.
7. Balatsoukas-Stimming, A., M. Bastani Parizi, and A. Burg, LLR-Based Successive Cancellation List Decoding of Polar Codes. IEEE Transactions on Signal Processing, 2015. 63(19): p. 5165-5179.
8. Arikan, E., Systematic Polar Coding. IEEE Communications Letters, 2011. 15(8): p. 860-862.
9. Vangala, H., Y. Hong, and E. Viterbo, Efficient Algorithms for Systematic Polar Encoding. IEEE Communications Letters, 2016. 20(1): p. 17-20.