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研究生:陳駿德
研究生(外文):CHEN,CHUN-TE
論文名稱:採用消息傳遞演算法的LDPC碼解碼循環效應之分析
論文名稱(外文):Analysis of cycle effect in the LDPC codes decoding with message passing algorithm
指導教授:李昌明李昌明引用關係
指導教授(外文):LEE, Chang-Ming
口試委員:李昌明邱茂清翁健家蘇益生
口試委員(外文):LEE, Chang-MingCHIU, MAO-CHINGWeng, Jian-JiaSU, YI-SHENG
口試日期:2023-07-28
學位類別:碩士
校院名稱:國立中正大學
系所名稱:通訊工程研究所
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:2023
畢業學年度:111
語文別:中文
論文頁數:64
中文關鍵詞:短長度循環訊息傳遞演算法低密度奇偶校驗碼循環影響
外文關鍵詞:short cyclesmessage passing algorithmslow-density parity-check (LDPC) codescycle effect
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低密度奇偶校驗碼 (LDPC codes) 在解碼採訊息傳遞演算法時,在校驗矩陣上短長度循環 (Short cycle) 的自我參照訊息易受錯誤影響,並隨迭代過程累積大量錯誤,以致大幅影響錯誤更正的效能,當採用較長的LDPC codes時,除了付出高計算複雜度的成本,短長度循環更會造成錯誤更正效果不彰,影響通訊品質更甚,例如5G 非地面波低軌道傳輸標準採 (8176,7156) 低密度奇偶校驗碼,所對應的校驗矩陣大小為1022 × 8176,其周長為6,對應長度為6循環 (6-cycle) 的數量就多達121618個,故採訊息傳遞的解碼計算應該不是很理想,但已商業化的標準卻不容輕率修正或更動。本論文提出一種基於NMSA (Normalized Min-Sum Algorithm) 與SPA (Sum-product Algorithm) 可消除循環對解碼效能影響的方法,此概念會修正傳統的訊息傳遞演算法,針對指定長度迴圈內的自我參照訊息調整。迴圈資料十分龐雜,為了降低錯誤訊息的累積,以有效的訊息計算並提升錯誤更正的效能,模擬結果顯示, BER比起NMSA最多可降低40%,比起SPA最多可以降低16%。
When decoding low-density parity-check codes (LDPC codes) with message-passing algorithms, short cycles in the parity check matrix can introduce self-referential messages and may cause more errors during the iterative process. For long LDPC codes, the high computational complexity and the short-length cycles can lead to poor error correction effects and affect the communication quality, especially for applications such as 5G non-terrestrial low-orbit transmission. For example, the (8176,7156) low-density parity-check code has a check matrix of size 1022 × 8176 and with girth=6. The number of 6-cycles is 121618. Therefore, the decoding process of information transmission is not ideal, but the commercialized standard cannot be easily modified or changed. This paper proposes a method based on NMSA (Normalized Min-Sum Algorithm) to eliminate the impact of loops on decoding performance by adjusting the self-reference message. The method can prevent the accumulation of errors, and improve the efficiency of error correction with accurate message calculation. The simulation results show that the method can reduce the BER by up to 40% compared to NMSA, and up to 16% lower than SPA (Sum-product Algorithm, SPA).
摘要 B
Abstract C
目錄 D
圖目錄 F
表目錄 H
第一章 緒論 - 1 -
1.1 數位通訊系統簡介 - 1 -
1.2 研究動機 - 2 -
第二章 低密度同位檢測碼 - 6 -
2.1 LDPC codes基本概念 - 6 -
2.1.1 線性區塊碼 - 7 -
2.1.2 同位檢測矩陣 - 8 -
2.1.3 規則型與非規則型LDPC codes - 11 -
2.1.4 循環與周長 - 11 -
2.1.5 非二位元LDPC codes - 13 -
2.2 LDPC codes建構方式 - 14 -
2.2.1 Gallager codes - 14 -
2.2.2 Mackay codes - 14 -
2.2.3 Qusai-cyclic (QC) LDPC codes - 15 -
2.3 LDPC codes編碼與解碼 - 17 -
2.3.1 LDPC codes編碼方式 - 17 -
2.3.2 LDPC codes解碼方式 - 17 -
2.4 循環搜尋相關研究 - 29 -
2.4.1 NP問題 - 29 -
2.4.2 訊息傳遞搜尋循環演算法 - 30 -
第三章 改進消息傳遞演算法設計 - 35 -
3.1 (6,3)矩陣的MSA範例 - 36 -
3.2 消除cycle訊息影響之演算法 - 38 -
第四章 模擬結果 - 42 -
4.1 408.3.854 LDPC codes (Mackay) - 42 -
4.2 矩陣短循環之連通性探討 - 47 -
4.3 演算法複雜度比較 - 50 -
第五章 結論與未來展望 - 51 -
參考文獻 - 52 -


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