近幾年來隨著智慧型手機的普及，QR碼 ( quick response code ) 已在生活中隨處可見，常常出現在廣告文宣的小角落，隨手一拍即可知曉業者想告知消費者的訊息。
QR碼，亦即快速反應碼，顧名思義，具有超高速判讀特性。雖然說QR碼非常方便迅速，但還是有很多業者喜歡在QR碼上面直接覆蓋自己商家的標誌( logo )來達到立即的廣告效益，更可以與其他商家有更多的區別性，但覆蓋的標誌大小有限，若覆蓋了過大面積的標誌，就會造成QR碼無法順利被解碼。
在本論文中我們提出新的QR碼編解碼方式，先將我們所需要的資訊透過標準QR碼編碼器進行編碼，決定好標誌大小及要擺放位置後，將QR碼中會被標誌破壞的位置(亦即會被標誌覆蓋的位置)之資料搬移至不會被標誌破壞的位置(亦即不會被標誌覆蓋的位置)之第二層位元層( LSB Bit plane)，使得原始一個模組( module )含有一個位元的傳統QR碼轉變成一個模組含有兩個位元的模組移置QR碼，再轉為四種不同的灰度值，完成編碼，也就是說，編碼完成後，會由原本只有黑白兩階的傳統QR碼轉換成有四階灰度的模組移置QR碼，本論文將這種模組移置QR碼簡稱為MDQR ( module–displaced QR code )。在解碼部分，我們所提出的模組移置QR碼也可以兼容於標準QR碼解碼器。當我們取得一個模組移置QR碼的影像後，先經過第一階段解碼，將此模組移置QR碼影像經過二值化並直接進入標準QR碼解碼器來進行解碼，如若第一階段解碼失敗再使用第二階段解碼，即使用我們所提出的模組移置QR碼解碼器進行解碼，此階段亦是本論文的重點。
由實驗結果可知，我們提出的方法是有效的，也就是說，使用我們所提出的模組移置QR碼，業者就可以突破傳統QR碼可加的標誌大小的限制來提供給消費者更多訊息。

Quick-Response (abbreviated as QR) codes can be regarded as an extension in bar code symbology. In recent years, they have found pervasive applications in our daily life, such as product item identification, product tracking, document management, scan-and-link webpage connection, and so on. Moreover, their popularity and function are growing in a fast pace. One of the most popular developments in various applications of QR codes is to embed logos into them, usually for cooperation identification, for easy interpretation by human, or even just for fun. Logo embedding, however, can cause high probability of failure when QR decoding is performed, especially when the logo is big (i.e. when the logo occupies a big part of the QR code). The issue of embedding logos into QR codes addressed in this thesis. Moreover, the corruption caused by noise, which occurs when the camera scanning/imaging of QR codes is performed, is also addressed.
In this thesis, a scheme that involves module displacement is proposed to deal with the embedding of a logo into a QR code. The basic idea is to move the data nodules that are corrupted by the logo to hide behind those modules that are not corrupted by the logo. How exactly the hiding is carried out? The trick is to convert the originally binary modules, which are either black or white, into four-level modules. In other words, each module can have hour different luminance levels (also known as gray levels), and thus can carry two bits. The data-carrying part (i.e. the modules that are not part of the function patterns and are not part of the function patterns and are not part of logo) of the QR code can thus be regarded an image consisting of two bit planes. The hiding place for those displaced modules is the LSB (least-significant-bit) bit plan, while the MSB (most-significant-bit) bit plan holds the original data modules that are not corrupted by the logo. The proposed scheme is called module-displaced QR (MDQR) code.
In the decoding of MDQR code, the image intensity, which is one of the four preset gray levels in QR encoding plus the additive noise (assumed to be Gaussian distributed), corresponding to each observed four-level module is converted to likelihood of the data bit-pair being 00,01,10, and 11. They are soft decisions. The soft decisions for the MSB bit plane are directly converted hard decisions, and they represent the data bits that originally reside in areas not occupied by the logo. The soft decision in the LSB bit plane, however, provide information about those data bits that originally reside in areas corrupted by the logo. Since one logo-corrupted data bit can be displaced into several logo-free positions, all the soft decisions should be combined to make the final hard decision for the bit. For the decoder, it is essential to know where the logo is in the MDQR code. In other words, the logo-location information is needed. This information is embedding into some alignment patterns. Simulations are conducted to test the effectiveness of the proposed MDQR scheme. It turns out that a large portion of originally field decoding becomes successful when the MDQR scheme is applied.

[1] Z. A., M. B., M. M. E. V., and N. A. C. A., “CQR codes: Colored quick-response codes,” 2012 IEEE International Conference on Consumer Electronics - Berlin (ICCE-Berlin), pp. 321 -- 325, 2010.
[2] L. A., Q. M., I. G., G. A., “High Capacity Colored Two Dimensional Codes,” Proceedings of the 2010 International Multiconference on Computer Science and Information Technology (IMCSIT), pp. 709 -- 716, 2010.
[3] D. Samretwit and T. Wakahara, “Measurement of Reading Characteristics of Multiplexed Image in QR Code,” 2011 Third International Conference on Intelligent Networking and Collaborative Systems (INCoS), pp. 552 -- 557, June 2011.
[4] “Information technology – Automatic identification and data capture techniques – Bar code symbology – QR Code,” International Standard ISO/IEC 18004, ISO/IEC, 2006.
[5] Z. L., T. H., R. W., X. Z., “A method of image analysis for QR code recognition,” 2010 International Conference on Intelligent Computing and Integrated Systems (ICISS), pp.250 -- 253, Oct. 2010.
[6] John G. Proakis, “Digital Communication” Ch5, pp231--319, September 1969.

[7] “Quick Response Code : Guidelines to Enable Data Capture for the Initiation of a SEPA Credit Transfer, ” Doc EPC069-12 , 13 December 2012.
[8] W. W. Peterson, “Encoding and error-correcting procedures for the Bose-Chaudhuri codes,” IEEE Trans. Inform. Theory, vol.20, pp. 459 -- 470, 1960.
[9] I. S. Reed and G. Solomon, “Polynomial Codes Over Certain Finite Fields,” Journal of the Society of Industrial and Applied Mathematics (SIAM), pp. 200 -- 204, June 1960.
[10] Sarwate, D. V., “High-speed architectures for Reed-Solomon decoders,” IEEE Circuits and Systems Society, pp. 641 -- 655, Oct. 2001.
[11] B. Sklar Digital Communications - Fundamental and Applications. Prentice-Hall International, 2001.