臺灣博碩士論文加值系統

LDPC(Low-Density Parity-Check)碼為下個世代的先進通訊標準所採用的錯誤更正碼，其優異的錯誤更正能力可以逼近Shannon的理論值，配合訊息傳遞(Message Passing , MP)演算法，可以快速得到傳送端所發出的訊息，雖然該演算法在解碼方面有很好的效能，但因為其複雜度偏高，所以，很多研究都在探討如何改善複雜度，又不會使其效能嚴重的衰減。在本論文中，基於和積演算法(Sum-Product algorithm , SPA)為軟式解碼法中最佳的解碼演算法，而針對此解碼法提出三種不同疊代分配的方式來做分析，調適的選擇出部份位元節點來替代所有的位元節點，減少其運算量，在疊代解碼失敗時，依所分配的疊代次數，增加位元節點的運算來更新檢查節點，其在最後幾次疊代時將回歸至Sum-Product演算法，有效的降低運算複雜度，在效能上也沒有嚴重的衰減。

LDPC code is an error-correcting code which is adopted for the next generation''s advanced communication standard. Its error-correcting ability may approach the Shannon’s theoretical value. With the MP algorithm, it can decode received samples in high speed from transmitter. This algorithm has a good performance in the decoding aspect, but its complexity is higher. Thus, many researchers discuss how to improve complexity without making the performance reduced seriously. In this thesis, the SPA(Sum-Product algorithm) is the best decoding algorithm in soft-decoding to aim at this decoding method which proposes three different ways in the distribution of iteration to do analysis. The method adjusts bit nodes to substitute all bit nodes, and reduces the quantity of operations. When the iteration decoding fails, we increase number of bit nodes and update the message of the check nodes according to the result of the iteration. Finally, its several iterations will return to Sum-Product algorithm. Therefore, it effectively reduces the complexity and without seriously weaken its performance.

中文摘要 I
Abstract II
目錄 IV
圖目錄 VI
表目錄 VIII
第一章 前言 1
1.1 研究內容與論文動機 1
1.2 論文組織 1
第二章 LDPC Code 2
2.1 線性區塊碼 2
2.1.1 線性區塊碼定義 2
2.1.2 生成矩陣與同位元檢查矩陣 3
2.1.3 漢明權重與漢明距離 6
2.2 LDPC Codes之介紹 8
2.2.1 LDPC Code定義 10
2.2.2 Tanner Graph 12
2.3 LDPC Codes之設計架構類型 13
2.3.1 隨機構造方法 13
2.3.1.1 規則性(Regular) LDPC Codes 14
2.3.1.2 不規則性(Irregular) LDPC Codes 14
2.3.2 代數構造方法 15
2.4 LDPC Codes之編碼法 17
第三章 解碼演算法 20
3.1 Message Passing演算法 21
3.1.1 Sum-Product algorithm 22
3.1.2 Min-Sum algorithm 29
3.1.3 Normalized BP-Based algorithm 30
3.1.4 Offset BP-Based algorithm 32
3.2 低複雜度解碼演算法 32
3.2.1 Algorithm 1 32
3.2.2 Algorithm 2 35
3.3 解碼演算法 37
3.3.1 動機 37
3.3.2 提出減少運算量的機制 37
第四章 模擬結果與分析 43
第五章 結論 54
參考文獻 55
附錄 57

[1] C. E. Shannon, “A Mathematical Theory of Communication,” Bell Syst. Tech. J., pp. 379-423(Part 1); pp. 623-56(Part 2), July 1948.
[2] R. G. Gallager, “Low-density parity-check codes,” IRE Trans. Inform. Theory, pp. 21-28, vol. 8, no. 1, Jan. 1962.
[3] R. G. Gallager, “Low-Density Parity-Check Codes,” MIT Press, Cambridge, MA, 1963.
[4] R. M. Tanner, “A recursive approach to low complexity codes,” IEEE Trans. Inform. Theory, vol. 74, no. 2, pp. 533-547, Sept. 1981.
[5] D. J. C. MacKay and R. M. Neal, “Near Shannon limit performance of low density parity check codes,” IEE Electron. Lett., vol. 32, no. 18, pp. 1645-1646, Aug. 1996.
[6] S. Y. Chung, G. D. Forney, T. J. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit,” IEEE Comm. Lett., vol. COMM-5, no. 2, pp. 58-60, Feb. 2001.
[7] D. J. C. MacKay, “Good error-correcting codes based on very sparse matrices”, IEEE Trans. Inf. Theory, 45, pp. 399–432, March 1999
[8] Y. Kou, S. Lin, and M. P. Fossorier, “Low-density parity-check codes based on finite geometries: a rediscovery and new results,” IEEE Trans. Inform. Theory, Vol. 47, no. 7, pp. 2711–2736, Nov. 2001.
[9] John L. Fan ,“Constrained coding and soft iterative decoding” Kluwer Academic Publishers, 2001.

[10] Kwangho Shin, Jungwoo Lee, “Low Complexity LDPC Decoding Techniques with Adaptive Selection of Edges,” in VTC2007, Apr. 2007, pp. 2205-2209.
[11] M. Miladinovic, M. P. C. Fossorier and H. Imai, “Reduced complexity iterative decoding of low-density parity check codes based on belief propagation,” IEEE Trans. Commun., Vol. 47, pp. 673-680, May 1999.
[12] J. Chen and M. P. C. Fossorier, “Near optimum universal belief propagation based decoding of low-density parity check codes,” IEEE Comm. Lett., Vol. 50, pp. 406-414, March 2002.
[13] Cavus. E, Daneshrad, B,“A Computationally efficient selective node updating scheme for decoding of LDPC codes,” in MILCOM 2005, Oct.2005, pp1375-1379.
[14] Eun-A Choi, Dae-IK Chang, Deock-Gil Oh, Electronics and Telecommunications Research Institute, Ji-Won Jung, Korea Maritime University, “Low Computational Complexity Algorithm of LDPC Decoder for DVB-S2 Systems,” in VTC05, Sep. 2005.
[15] 林銀議, “數位通訊原理 編碼與消息理論,” 五南, 2005.
[16] David J.C MacKay:Cavendish Laboratory, Cambridge. Get from http://www.inference.phy.cam.ac.uk/mackay/codes/data.html