本論文基於理論模型的設計，整合繞射影像輸出與多頁資料編碼，並充分考量讀取過程中因光學擴散（Blur）與雜訊所造成的影響，在資料編碼端，我們利用以前論文所建立的不同點亮個數並排除高錯誤率圖樣的稀疏碼表，使每個四乘四稀疏碼區塊的資訊容量由原本九位元提升至最多十三位元，同時降低光學擴散導致的錯誤。
本研究可分為兩部分：第一部分針對已知光學擴散資訊，分別設計對應的解碼法，分析模糊與雜訊的聯合作用，並結合低密度奇偶檢查碼(Low-density parity-check code，LDPC )進行編解碼。此外，我們提出邊界感知解碼法，利用已解碼區塊的擴散邊界畫素作為先驗資訊，顯著提升模糊資訊的精度。第二部分則進一步將LDPC解碼過程中的迭代機率更新機制，應用於稀疏碼與無稀疏碼的情況，並於無稀疏碼情況下搭配編碼端間隔儲存策略，有效抑制光學擴散對系統性能的影響。實驗結果顯示，所提方法在多種模糊與雜訊條件下皆能顯著降低位元錯誤率，提升全像光儲存系統的可靠性與容錯能力。

This thesis is based on a theoretical model design that integrates diffraction image output with multi-page data encoding, while fully accounting for the effects of optical blur and noise during the reading process. On the encoding side, we adopt previously developed sparse code tables with different numbers of activated pixels, excluding high-error patterns. This increases the information capacity of each 4×4 sparse code block from 9 bits to as many as 13 bits, while simultaneously reducing errors caused by optical blur.
The study is divided into two parts. In the first part, decoding methods are designed for known blur conditions to analyze the joint impact of blur and noise, combined with low-density parity-check (LDPC) coding and decoding. In addition, we propose a boundary-aware decoding method that leverages the blurred boundary pixels of previously decoded blocks as prior information, thereby significantly enhancing the accuracy of blur compensation. In the second part, we further incorporate an iterative probability update mechanism within the LDPC decoding process, applying it to both sparse-coded and non-sparse-coded cases. For the non-sparse-coded case, we also adopt an interleaving storage strategy at the encoding stage to effectively suppress the impact of optical blur on system performance.
Experimental results demonstrate that the proposed methods can substantially reduce the bit error rate under various blur and noise conditions, thereby improving the reliability and fault tolerance of holographic data storage systems.

[1] Kevin Curtis, Lisa Dhar, William Wilson, Adrian Hill, Mark Ayres, “Holographic Data Storage: From Theory to Practical Systems”, 2009.
[2] Yeh-Wei Yu, Yuan-Cheng Chen, Kun-Hao Huang, Chih-Yuan Cheng, Tsung-Hsun Yang, Shiuan-Huei Lin, and Ching-Cherng Sun, “Reduction of phase error on phase-only volume-holographic disc rotation with pre-processing by phase integral”, Optics Express, Vol. 28, No. 19, Jul, 2020.
[3] Sarah J. Johnson, “Introducing Low-Density Parity-Check Codes”, School of Electrical Engineering and Computer Science, The University of Newcastle Australia, May, 2010.
[4] K. Deergha Rao, “Channel Coding Techniques for Wireless Communications Second Edition”, Springer, 2015.
[5] 陳震瑜, “高速成像通訊系統可行性之研究” ,國立中央大學光電科學工程學系, 碩士論文, 九月, 2021.
[6] 徐睿謙,“用於高速成像通訊系統之不同速率編碼”,國立中央大學通訊工程研究所, 碩士論文, 六月, 2022.
[7] Qin Yu, Fei Wu, Meng Zhang, Yahui Zhao, Chang Sheng Xie, “Improving reliability using phase distribution aware LDPC code for holographic data storage”, Applied Optics, Vol. 61, No. 21, July, 2022.
[8] Ya Hui Zhao, Fei Wu, Xiao Lin, Jian Zhou, Meng Zhang Qin Yu, Xiaodi Tan, Chang Sheng Xie, “Improving the data reliability of phase modulated holographic storage using a reliable bit aware low-density parity-check code”, Optics Express, Vol. 30, No. 21, October, 2022.
[9] Pilsang Yoon, Biwoong Chun, Haksun Kim, Jooyoun Park, Gwitae Park “Low-Density Parity-Check Code for Holographic Data Storage System with Balanced Modulation Code”, J. Appl. Phys, Vol. 47, No. 7, 2008.
[10] Hideki Hayashi, Kazuhiko Kimura, “Low-Density Parity-Check Coding for Holographic Data Storage”, J. Appl. Phys, Vol. 44, No. 5B, 2005.
[11] Jinyoung Kim, Jaejin Lee, “Two-Dimensional SOVA and LDPC Codes for Holographic Data Storage System”, IEEE TRANSACTIONS ON MAGNETICS, VOL. 45, NO. 5, May, 2009.
[12] 劉宜鈞,“全像光資訊儲存系統的編解碼”,國立中央大學通訊工程研究所, 碩士論文, 六月, 2024.
[13] Thomas J. Richardson, Rüdiger L. Urbanke, “Efficient encoding of low-density parity-check codes”, IEEE Transactions on Information Theory, Vol. 47, No. 2, pp. 638–656, February, 2001.
[14] Robert G. Gallager, “Low-density parity-check codes”, IRE Transactions on Information Theory, Vol. 8, No. 1, pp. 21–28, January, 1962.
[15] Masaki P. C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices”, IEEE Transactions on Information Theory, Vol. 50, No. 8, pp. 1788–1793, August, 2004.