臺灣博碩士論文加值系統

隨著科技的進步與便利，許多的應用上都會需要使用到圖像傳輸。由於圖像的像素有位元不等的特性，所以在圖像傳輸上時常使用不平等錯誤保護(UEP)的技術。現有的文獻中有許多方式結合不平等錯誤保護的研究，例如與渦輪碼結合或是與低密度同位檢測碼結合。
近年來，出現了一種新的更正碼技術，稱為極化碼。由於它的特性是透過通道建構找出好的通道進而傳輸訊息，得以使得它成為5G的通信標準之一。由於極化碼是最近新興的更正碼技術，且其在圖像傳輸方面的研究文獻並不多，所以我們想將極化碼和不平等錯誤保護等技術用於圖像傳輸並進行相關的研究。
本論文提出利用極化碼與不平等錯誤保護來進行圖像的傳輸。在極化碼中，通道的建構是一個很重要的步驟，它關係到我們所選擇傳輸的通道好壞。在我們的方法中，我們使用高斯近似(GA)所建構出的通道排序提出了四種狀況的探討，分別是圖像資料沒有做UEP並做GA排序、圖像資料有做UEP並做GA排序、圖像資料沒有做UEP並做自然順序和本論文所提出的圖像資料有做UEP並做自然順序。最後我們在一定範圍的訊雜比區間，提出了利用中位數濾波器以消除圖像上的胡椒鹽雜訊以提升PSNR值及其視覺效果。相較於其它極化碼用於圖像傳輸的方法，本論文不僅提升了還原圖像的PSNR值，更大大的改善還原的圖像，使其在中低訊雜比時就能有良好的視覺效果。

With the advancement and convenience of technology, image transmission is required for many applications. Since the pixels of the images have different weight of bits, we usually use unequal error protection (UEP) to transmit the images. There are many ways to combine UEP for use in image transmission in the existing literature, such as combining with turbo codes or LDPC codes.
In recent years, there has been a new error correction scheme called polar codes. Polar codes use code construction to find out which channels are good for transmitting the information. Due to their good property, polar codes have become one of the 5G communication standards. Because polar codes are the latest emerging error correction code, and also because there are not much research on polar codes with image transmission, we want to study the combination of polar codes and UEP for image transmission.
It is a key issue to do code construction for polar codes, because we need to find out good channels for sending the information bits. In our method, we use Gaussian approximation (GA) to construct the channel and propose four kinds of situations to simulate: image using GA-sorted order, image with UEP using GA-sorted order, image using natural order and image with UEP using natural order. At the end, in order to improve the visual effect of the recover image within a SNR range, we will use median filter to filter out the salt-and-pepper (SAP) noise in the image. Compared with others, our method propose the recovers images to get higher PSNR and better visual effect at low-to-medium SNR range.

摘要……………………………………………………………………….i
Abstract…………………………………………………………………..ii
致謝……………………………………………………………………...iii
目錄……………………………………………………………………...iv
圖索引…………………………………………………………………..vii
中英文對照表…………………………………………………………...xi
第一章 緒論……………………………………………………………..1
1.1 前言……………………………………………………………..1
1.2 不平等的錯誤保護……………………………………………..1
1.3 Polar code……………………………………………………….2
1.4 研究動機………………………………………………………..2
1.5 論文章節………………………………………………………..3
第二章 Polar code的背景介紹…………………………………………4
2.1 通道結合和通道分裂…………………………………………..4
2.1.1 通道結合…………………………………………………5
2.1.2 通道分裂…………………………………………………7
2.2 通道極化………………………………………………………10
2.3 編碼……………………………………………………………12
2.4 解碼……………………………………………………………13
第三章 利用不平等錯誤保護進行圖像傳輸 ………………………...18
3.1 系統架構………………………………………………………19
3.2 使用UEP來進行圖像傳輸…………………………………...21
3.3 基於高斯近似之通道建構……………………………………24
3.4 訊息位元放入Polar code編碼的排序……………………….31
3.4.1 高斯近似排序順序……………………………………..31
3.4.2 自然順序………………………………………………..33
3.5 列表解碼………………………………………………………34
3.6 中位數濾波器…………………………………………………37
第四章 實驗結果與討論………………………………………………38
4.1 圖像傳輸的實驗結果…………………………………………39
4.1.1 Polar code不同碼長對還原圖像結果之比較………….39
4.1.2 高斯排序順序和自然順序對還原圖像之結果比較…..46
4.1.3 由LSB跟MSB觀察圖像之位元錯誤率……………...50
4.2 還原圖像與套用中位數濾波器之實驗結果…………………52
4.2.1 經過中位數濾波器的圖像之視覺效果比較…………..52
4.2.2 經過中位數濾波器的圖像之PSNR比較……………..62
第五章 結論與未來展望………………………………………………68
參考文獻………………………………………………………….…….71

[1] E. Arikan, “Channel Polarizaion: A Method for Constructing Capacity Achieving Codes for Symmetric Binary-Input Memoryless Channels,” IEEE Trans. Inf. Theory, vol. 56, no. 7, pp. 3051-3073, Jul. 2009.

[2] E. Arikan, “A Performance Comparison of Polar Codes and Reed-Muller Codes,” IEEE Comm. Letters, vol. 12, pp. 447-449, June. 2008.

[3] W. Du, S. Zhang, and F. Ding, “Exploiting the Uep Property of Polar Codes to Reduce Image Distortions Induced by Transmission Errors,” in 2015 IEEE/CIC International Conference on Communications in China (ICCC), pp. 1–5, Nov. 2015

[4] S. Y. Chung, T. Richardson, and R. Urbanke, “Analysis of Sum-Prodcut Decoding of Low-Density-Parity-Check Codes Using a Gaussian Approximation,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 657-670, Feb. 2001.

[5] R. Mori and T. Tanaka, “Performance and Construction of Polar Codes on Symmetric Binary-Input Memoryless Channels,” 2009 IEEE International Symposium on Information Theory, Seoul, pp.1496-1500, July. 2009.

[6] R. Mori and T. Tanka, “Performance of Polar Codes with the Construction Using Density Evolution,” IEEE Communications Letters, vol. 13, no. 7, pp. 519-521, July. 2009.

[7] T. Richardson and R. Urbanke, “Modern Coding Theory”. Cambridge University Press, 2008.

[8] I. Tal and A. Vardy, “List Decoding of Polar Codes,” IEEE transactions on information theory, vol. 61, no. 5, pp. 2213-2226, May. 2015.

[9] Gonzalez, R.C., Woods R.E., and Eddins S. L., “Digital Image Processing Using MATLAB” , 2nd Edition, McGraw-Hill, 2011.

[10] 鐘國亮, “影像處理與電腦視覺(第六版)”東華書局, 2016.