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研究生:李承諺
研究生(外文):LEE, CHENG-YEN
論文名稱:極化碼之簡化連續消除解碼效能研究
論文名稱(外文):The Research on Simplified Successive Cancellation Decoding Performance for Polar Codes
指導教授:翁萬德
指導教授(外文):Weng, Wan-De
口試委員:夏郭賢陳永隆
口試委員(外文):XIA,GUO-XIANCHEN,YONG-LONG
口試日期:2022-07-06
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:2022
畢業學年度:110
語文別:中文
論文頁數:68
中文關鍵詞:極化碼通道極化現象連續消除解碼簡化連續消除解碼置信傳播解碼
外文關鍵詞:polar codechannel polarizationsuccessive cancellationsimplified successive cancellationbelief propagation
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  • 被引用被引用:0
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  • 下載下載:32
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摘要
隨著人們對於超高可靠度與低延遲的通訊需求日益提升,現今極化碼(polar code)的表現已經非常接近頻道上進行無差錯傳輸的理論最大傳輸速率值,也就是所謂的香農極限(Shannon limit)。而通道的編解碼技術是無線通訊的核心技術,所以在5G系統中的增強型行動寬頻通訊(enhanced mobile broadband, eMBB)就有使用到極化碼,因而極化碼成為5G通訊重要的技術之一。
本文主要研究極化碼連續消除解碼(successive cancellation, SC)以及簡化連續消除解碼(simplified successive cancellation, SSC) 與置信傳播(belief propagation, BP)解碼在不同碼長以及碼率來做模擬,並進行模擬分析及驗證。
在進行延時的模擬與分析後,可以發現SC解碼與SSC解碼在解碼誤碼率(bit error rate, BER)上沒有太大的差異,但SSC解碼確實能夠比SC解碼有更好的解碼速率,在碼長256、512、1024下,當碼率為0.6時,解碼平均快了40%;當碼率為0.8時,解碼速度平均快了30%。因為SSC在凍結位元節點與訊息位元節點的簡化,在BER性能一樣的條件下,SSC解碼有更低的計算複雜度而有更快的解碼速度,比起SC解碼更適合被應用。



關鍵字:極化碼,通道極化現象,連續消除解碼,簡化連續消除解碼,置信傳播解碼

ABSTRACT
The demand for ultra-reliable and low-latency communication has been significantly increasing in these decades. Channel coding is one of the core technologies in wireless communication systems. It has been demonstrated that the performance of polar code is very close to the theoretical maximum transmission rate value for error-free transmission on the channel, that is, the Shannon limit. Polar code, therefore, has become one of the important technologies of 5G communication. For example, it is used in the enhanced mobile broadband communication (eMBB) in 5G system.
This thesis is mainly focused on the study of decoding strategy of polar codes. The simulation analysis and comparison of three decoding methods, namely, successive cancellation (SC), simplified successive cancellation (SCC) and belief propagation (BP), will be presented.
It can be seen from simulation results that SC and SSC decoders are very close in average bit error rate (BER) performance. But the calculations on frozen bit nodes and message bit nodes are simplified in SSC decoder, so lower computational complexity and faster decoding speed over SC can be achieved. Simulations have been performed for code lengths of 256, 512, and 1024. It is seen that the decoding speed of SSC is 40% and 30% faster than SC when code rate is 0.6 and 0.8, respectively. This concludes that SSC is more suitable for applications than SC decoding.



Keywords: polar code, channel polarization, successive cancellation, simplified successive cancellation, belief propagation

目錄
摘要 ii
ABSTRACT iii
誌謝 iv
目錄 v
表目錄 vii
圖目錄 viii
第一章 緒論 1
1.1研究背景 1
1.2研究目的與方法 2
1.3論文架構 2
第二章 極化碼 3
2.1 極化碼預備知識 3
2.1.1 B-DMC結構 3
2.1.2 陪集碼 6
2.2 通道極化 7
2.2.1 通道組合 8
2.2.2 通道分離 13
2.2.3 通道極化效應模擬示意圖 15
2.3 編碼原理 17
2.4 極化碼解碼原理 22
2.4.1 BP解碼 22
2.4.2 BP解碼原理 22
2.5 SC解碼原理 25
2.5.1 SC解碼範例 27
2.5.2 SC解碼結論 32
2.6 SSC解碼 33
2.6.1 SSC解碼延時計算 36
2.6.2 SSC解碼結論 38
第三章 模擬結果與數據分析 39
3.1 極化碼解碼效能之研究方法 39
3.2 編碼增益 40
3.3 實驗結果與分析 41
3.3.1 SC、SSC和BP三種解碼分析 41
3.3.2 SSC固定碼率0.6三種碼長下的位元錯誤率 42
3.3.3 SSC固定碼率0.8三種碼長下的位元錯誤率 46
3.3.4 運算量比較 52
3.3.5延時模擬分析 54
第四章 結論與未來展望 56
參考文獻 57


參考文獻
[1]E. Arikan, “Channel Polarization: A Method for Constructing Capacity-Achieving Codes,” IEEE International Symposium on Information Theory, pp.1173-1177, 2008.
[2]A.A.Yazdi and Frank R. Kschischang, Fellow, “A Simplified Successive-Cancellation Decoder for Polar Codes,” IEEE Communications Letters, VOL. 15, NO. 12, Dec. 2011
[3]N. Hussami, S. Korada and R. Urbanke, “Performance of Polar Codes for Channel and Source Coding,” IEEE International Symposium on Information Theory, pp.1488-1492, 2009.
[4]H. Zhiliang, “Research on Encoding and Decoding Methods for Polar Codes,” Ph. D. thesis, Southeast University, pp.1-10, May. 2013.
[5]E. Arikan, “Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels”, IEEE Transactions on Information Theory, vol.55, Issue.7, pp.3051-3073, 2009
[6]B. Yuan and K. K. Parhi, “Early Stopping Criteria for Energy-Efficient Low-Latency Belief-Propagation Polar Code Decoders”, IEEE Transactions. Signal Process., vol. 62, no. 24, pp. 6496-6506, Dec. 2014.
[7]S. M. Abbas, Y. Fan, J. Chen and C.-Y. Tsui, “High-Throughput and Energy-Efficient Belief Propagation Polar Code Decoder”, IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 25, no. 3, pp. 1098-1111, Mar. 2017.
[8]G. D. Forney, “Codes on Graphs: Normal Realizations,” IEEE Transactions on Information Theory, vol.47, pp.520-548, Feb. 2001.
[9]R. Tanner, “A Recursive Approach to Low Complexity Codes,” IEEE Transactions on Information Theory, vol.27, pp.533-547, Sep. 1981.
[10]D. J. C. MacKay, “Good Error-Correcting Codes Based on Very Sparse Matrices,” IEEE Transactions on Information Theory, vol. 45, pp. 399–431, Mar. 1999.
[11]D. J. C. Mackay and R. M. Neal, “Near Shannon Limit Performance of Low Density Parity Check Codes,” Electronics Letters , vol.32, pp.1645-1646, Aug. 1996.
[12]T. J. Richardson, M. A. Shokrollahi and R. L. Urbanke, “Design of Capacity-Approaching Irregular Low-Density Parity-Check Codes,” IEEE Transactions on Information Theory, Vol. 47, pp.619-637, Feb. 2001.
[13] A.Yazdi and R.schischang “A Simplified Successive-Cancellation Decoder
for Polar Codes” IEEE Communications Letters , Vol. 15, pp.1378-1380 Issue:12, December. 2011.

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