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研究生:李仲澤
研究生(外文):LI,ZHONG-ZE
論文名稱:類下三角LDPC正規化補償式最小和演算法編解碼之硬體實現
論文名稱(外文):Hardware Realization of Normalized Offset Min-Sum Algorithm for Approximate Lower Triangular LDPC Encoder and Decoder
指導教授:翁萬德
指導教授(外文):WENG,WAN-DE
口試委員:竇奇陳永隆
口試委員(外文):DOU,CHIECHEN,YOUNG-LONG
口試日期:2017-07-06
學位類別:碩士
校院名稱:國立雲林科技大學
系所名稱:電機工程系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2017
畢業學年度:105
語文別:中文
論文頁數:65
中文關鍵詞:低密度同位元檢查碼類下三角編碼最小和演算法
外文關鍵詞:LDPC codeapproximate lower triangle encoderMSA
相關次數:
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  • 下載下載:2
  • 收藏至我的研究室書目清單書目收藏:0
1962年低密度同位元檢查碼(low-density parity check code, LDPC code)被提出時,證明了其錯誤更正能力非常接近薛農極限(Shannon limit),由於當時技術尚未成熟並未受到太大的重視。直到90年代,積體電路技術開始進步,低密度同位元檢查碼的實作逐漸可行,且低密度同位元檢查碼在硬體實現成本較低,LDPC碼才又被人們廣泛討論及應用。

在本論文詳細介紹LDPC碼中的類下三角編碼與正規化補償式最小和演算法(normalized offset min-sum algorithm, NOMSA)解碼,相較於最小和演算法(min-sum algorithm, MSA)並沒有增加太多計算量,就可提升其效能,使其效能夠更接近理論上公認最優秀的對數領域和積演算法(Log-Domain SPA)。本論文使用硬體描述語言,在高斯白雜訊(AWGN)的環境下進行位元錯誤率分析,並觀察其位元錯誤率曲線。

我們找出最佳的參數設定,將NOMSA的補償係數μ設為0.1,正規化因子ν設為0.6。在迭代次數皆為5次的情況下,位元錯誤率為10-4時,NOMSA與MSA效能相比大約改善了0.3 dB,且成功將NOMSA效能提升與對數領域和積演算法(Log-Domain SPA)剩0.9 dB差距。

Low-density parity-check (LDPC) code was proposed in 1962, and it has been shown its error correcting capability almost approaches the Shannon limit. LDPC code did, however, not obtain much attention due to the technology is not yet mature. Until the 1990s, with the improvement of integrated circuit technology, the implementation of LDPC code has become feasible and the LDPC codes demand relatively lower hardware cost. LDPC codes have thus been widely discussed and applied.

This thesis presents a detailed description about the application of approximate lower triangle encoder and normalized offset min-sum algorithm (NOMSA) for LDPC decoder. Comparing with the min-sum algorithm (MSA), NOMSA can effectively improve system performance without adding too much excessive computational burden. It presents much closer performance to that of a Log-Domain SPA, which is recognized as the theoretically optimal solution. This thesis uses hardware description language to implement the encoder and decoder. The bit error rate analysis is performed through an additive white Gaussian noise (AWGN) environment.

To achieve the best decoding performance, we set the offset constant μ to be 0.1 , and the normalization factor ν to be 0.6 . When maximum numbers of iterations are chosen to be 5, simulation result shows that the coding gain of NOMSA is 0.3 dB over MSA at the bit error rate of 10-4. The performance gap between NOMSA and Log-Domain SPA has been successfully reduced to about 0.9 dB.

摘要 i
ABSTRACT ii
誌謝 iii
目錄 iv
表目錄 vi
圖目錄 vii
第一章 緒論 1
1.1 前言 1
1.2 研究目的 2
1.3 研究方法 3
1.4 各章節提要 3
第二章 低密度同位元檢查碼原理 4
2.1 低密度同位元檢查碼簡介 4
2.2 類下三角編碼 5
2.3 低密度同位元檢查碼解碼 9
2.3.1 Tanner圖 9
2.3.2 訊息傳遞演算法 11
2.3.3 和積演算法(sum product algorithm, SPA) 12
2.3.4 Log-Domain和積演算法(Log-Domain SPA ) 19
2.3.5 最小和演算法(Min-Sum Algorithm, MSA ) 24
2.3.6 補償式最小和演算法(Offset-Min-Sum Algorithm, OMSA) 27
2.3.7 正規化補償式最小和演算法(Normalized-Offset-Min-Sum Algorithm, NOMSA) 29
2.3.8 各演算法優缺點比較 32
第三章 LDPC碼實驗結果與效能分析 33
3.1 模擬背景 33
3.2 類下三角LDPC編碼介紹 33
3.3 類下三角LDPC解碼介紹 41
3.3.1 補償係數分析 46
3.3.2 正規化因子分析 47
3.4 不同參數時性能比較 48
3.5 位元錯誤率分析圖 50
第四章 結論與未來展望 53
參考文獻 54



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[8]T.J.Richardson, and R.L.Urbanke,“Efficient Encoding of Low-Density Parity-Check Codes,”IEEE Transactions on Information Theory,Vol. 47, pp. 638-656, February, 2001.

[9] R.M.Tanner, “A Recursive Approach to Low Complexity Codes,” IEEE Trans. Inform. Theory, vol. IT-27, pp. 533-547, 1981.

[10]黃耀哲,“用於低密度同位元檢查碼之改良式適應性補償解碼演算法,” 國立成功大學電腦與通訊工程研究所 , 碩士論文 , 2007.

[11] M. P. C. Fossorier, M. Mihaljevic,and H. Imai, “Reduced Complexity Iterativedecoding of Lowdensity Parity Check Codes Based on Belief Propagation,” IEEE Trans. Commun., vol.47, pp.673-680, May.1999.

[12] M. Zhuo ,L. Ying and W. Xinmei ,“A Quasi-Parallel Encoder of Quasi-Cyclic LDPC Codes in IEEE 802.16e” 2009.

[13] J. Chen and M. P. C. Fossorier, “Near-Optimum Universal Belief Propagation BasedDecoding of Low-Density Parity Check Codes,” IEEE Trans. Commun, vol. 50, no. 3,pp 406-414, Mar. 2002.

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