信道极化和极化码版本2针对学生

1、极化码极化码( (Polar codes) )达到信道容量的编码方案黄志亮讨论组安排讨论组安排赵頔汪宇左德遥张施怡基本要求：基本要求：做ppt外行也能明白1. 讨论前一到两天把ppt发给所有人讨论内容：讨论内容：内容不限可以是自己所做的工作可以是阅读某篇或几篇文章的心得可以近期所看书籍的心得1.可以是近期碰到的问题？戚河平？姚松林？俞泓帆分组待定分组和顺序分组和顺序The Road to Channel Capacity信道极化和极化码信道极化和极化码代表文章： Erdal Arikan, Channel Polarization: A Method for Constructing Capa

2、city-Achieving Codes for Symmetric Binary-Input Memoryless Channels, IEEE Trans. on Information Theory, vol. 55, no. 7, pp. 3051-3073, July 2009. 由于这篇文章获得的奖励：The 2010 IEEE Information Theory Paper award is presented to Erdal Arikan.Kadir Has Outstanding Achievement Award is presented to Erdal Arikan

3、 for an invention that answers 60-year-old unsolved problem in information theory and communication engineering. The Institute of Electrical and Electronics Engineers (IEEE) has named Prof. Erdal Arkan an IEEE Fellow for his extraordinary work in contributions to coding theory. 1. We congratulate Pr

4、of. Erdal Arkan who received the prestigious 2013 IEEE W.R.G. Baker Award for his contribution to information theory. Erdal Arikan，Born in Ankara, Turkey, in 1958. B. S. degree from California Institute of Technology.S.M. and Ph.d. degrees from the Massachusetts Insititute of Technology.极化码意义极化码意义极化

5、码（Polar Codes） 信息论和编码领域顶级期刊(IEEE Trans on IT)2010的最佳论文奖 某种程度上说，完成了自信息论提出60年来信道编码理论家们的梦想 近十多来信息论和编码领域最激动人心的工作 在各种不同的场景下，渐进性能达到香农限，并且有着低的复杂度 Erdal Arikan和我和我信道：概率模型信道：概率模型 - 达到容量达到容量一一信道：信道举例信道：信道举例 - 达到容量达到容量二二信道编码定理信道编码定理 - 达到容量达到容量三三码率：码率：R = K/N，误码率：误码率：Pe 信道容量：信道容量：C=maxp(x)I(X;Y)（bits per transm

6、ission）（二进制输入）信道编码定理：（二进制输入）信道编码定理： 无差错传输条件下（无差错传输条件下（Pe=0），最大可达码率为），最大可达码率为CEb/N0=0.188dB，C=0.5：Eb/N0=0.188dB的的BiAWGN信道，无差错传输条件下，无论如信道，无差错传输条件下，无论如何设计编码器和译码器，何设计编码器和译码器， R最大只能到最大只能到0.5。汉明码LDPC码极化码LDPC码性能展示码性能展示- 达到容量达到容量四四From paper: Yu Kou, Shu Lin, “Low-Density Parity-Check Codes Based on finite

7、geometries： A Rediscovery and New Results”, IEEE Trans. Infor. Theory, Vol 47, No 7, Nov 2001极化码极化码- 达到容量达到容量五五From paper: Erdal Arikan, Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels, IEEE Trans. on Information Theory, vol. 55

8、, no. 7, pp. 3051-3073, July 2009. Erdal Arikan利用信道极化现象，从理论上严格证明了如下结论： 对于任意的二进制离散无记忆对称（B-DMS）信道，当码长趋向于无穷时，极化码可以达到信道容量（也即误码率趋向于零时，其码率R可以任意接近信道容量C），并且有着低的编译码复杂度。State of the art (polar codes)极化码和当前的最先进的技术有着相当或更好的性能。From paper: Ido Tal and Alexander Vardy, “List Decoding of Polar codes”, IEEE Trans. In

9、for. Theory, Vol 61, No 5, May 2015.极化码研究现状：国内研究极化码研究现状：国内研究（1）北京邮电大学K. Chen, K. Niu, and J. R. Lin, “List successive cancellation decoding of polar codes,” Electron. Lett., vol. 48, no. 9, pp. 695-697, Apr. 2012.K. Niu and K. Chen, “Stack decoding of polar codes,” Electron. Lett., vol. 48, no. 12,

10、pp. 500-501, Jun. 2012.K. Niu and K. Chen, “CRC-aided decoding of polar codes,” IEEE Commun. Lett., vol. 16, no. 10, pp. 1668-1671, Oct. 2012.K. Chen, K. Niu, and J. R. Lin, “Improved successive cancellation decoding of polar codes,” IEEE Trans. Commun., vol. 61, no. 8, pp. 3100-3106, Aug. 2013.“Bey

11、ond turbo codes: Rate-compatible puntured polar codes.” ICC 20131. 国家自然科学基金面上项目：信道极化码设计与优化研究 2012.1-2015.12极化码研究现状：国内研究极化码研究现状：国内研究（2）南京邮电大学Polar lattices: where Arikan meets Forney. ISIT 2013On the analysis of multiplicative-repetition codes and polar codes over binary erasure channels. WCSP 2012Co

12、operative coding scheme using polar codes. 2012 ICCSNTPerformance of polar codes on wireless communication channels. ICCT 2012Polar codes and its application in speech communications. WCSP 2011Encrypted polar codes for wiretap channel. 2012 ICCSNT1. Designs of Bhattacharyya parameter in the construc

13、tion of polar codes. 2011 WiCOM极化码研究现状：国内研究极化码研究现状：国内研究（3）中南大学1. A novel channel polarization on binary discrete memoryless channels. 2010 ICCS（4）北京航空航天大学1. A novel rate-adaptive distributed source coding scheme using polar codes. 2013, Communications Letters, IEEE （5）浙江大学On the polar codes for MIMO

14、. WCSP 20131. Polar code with Block-length N=3n . WCSP 2012（6）华为公司An adaptive successive cancellation list decoder for polar codes with cyclic redundancy check. 2012, Communications Letters, IEEE 极化码研究现状：国内研究极化码研究现状：国内研究（7）浙江师范大学Z.L. Huang, C.J. Diao and M. Chen, “Latency Reduced Method for Modified

15、 Successive-Cancellation Decoding of Polar Codes”, Electronics Letters, Vol. 48, No. 23, pp. 1505-1506, Nov. 2012.Zhiliang Huang, Chunjuan Diao, Jianxin Dai, Chunjiang Duanmu, Xia Wu and Ming Chen, “An Improvement of Modified Successive-Cancellation Decoder for Polar Codes”，IEEE Communications Lette

16、rs. 2013Zhiliang Huang, Chunjuan Diao, and Ming Chen, “Multiple Candidates Successive-Cancellation Decoding of Polar Codes”, （WCSP2012）, Huangshan, China. 黄志亮，陈明，极化码的编译码方法研究，博士学位论文，东南大学，20131. 国家自然科学青年基金项目：高维核矩阵信道极化码设计和译码算法优化 2015.1-2017.12极化码研究现状极化码研究现状：国外研究国外研究2EPFL：洛桑联邦理工学院洛桑联邦理工学院 瑞士瑞士Rdiger Urb

17、anke: Dr. Urbanke is a recipient of a Fulbright Scholarship. He is a co-author of the book “Modern Coding Theory” published by Cambridge University Press a co-recipient of the 2002 and the 2013 IEEE Information Theory Society Paper Award, the 2011 IEEE Koji Kobayashi Award, as well as the 2014 IEEE

18、Hamming Medal.代表文章：S. B. Korada, E. Sasoglu, and R. Urbanke. “Polar codes: characterization of exponent, bounds, and constructions”, IEEE Trans. Information Theory, 2010S. B. Korada and R. Urbanke, “Polar codes are optimal for lossy souce coding”, IEEE Trans. Information Theory, 20101. S. B. Korada,

19、 PHD Thesis: Polar codes for channel and source coding.极化码研究现状极化码研究现状：国外研究国外研究3Emre Telatar文章“Capacity of Multi-Antenna Gaussian Channels“,European Trans. Telecom., Nov. 1999的作者，被引用了10147次代表文章:E. Saaoglu, E. Telatar, and E. Arikan, “Polarization for arbitrary discrete memoryless channels,” in Proc.

20、IEEE Inf. Theory Workshop (ITW), Taormina, Italy, Oct. 2009, pp. 144-148.M Karzand and E Telatar, “Polar codes for q-ary source coding.” Information Theory Proceedings (ISIT), 2010 IEEE International Symposium on Information Theory. 1. R. Pedarsani, S. H. Hassani, I. Tal, and E. Telatar, “On the con

21、struction of polar codes,” in Proc. IEEE Int. Symp. Inform. Theory (ISIT), Saint-petesburg, Russia, Jul./Aug. 2011, pp. 11-15.极化码研究现状极化码研究现状：国外研究国外研究4加州大学圣地亚哥分校（加州大学圣地亚哥分校（University of California-San Diego）Ido Tal and Alexander Vardy代表文章：I. Tal and A. vardy, “How to construct polar codes,” IEEE Tra

22、ns. on Information Theory, vol. 59, no. 10, pp. 6562-6582, Oct 2013.I. Tal and A. Vardy, “List decoding of polar codes,” in Proc. IEEE Int. Symp. Inform. Theory (ISIT), Saint-Petesburg, Russia, Jul./Aug. 2011.极化码文章发表情况极化码文章发表情况上次报告：上次报告：2013年底年底 用用IEEExpolare搜索搜索”polar codes”一共有一共有183篇篇 在在上

23、搜索上搜索”polar codes”一共有一共有124篇篇 IEEE Trans. on Information Theory上一共上一共15篇篇本次报告：本次报告：2016年年9月月 用用IEEExpolare搜索搜索”polar codes”一共有一共有477篇篇 在在上搜索上搜索”polar codes”一共有一共有249篇篇 IEEE Trans. on Information Theory上一共上一共37篇篇极化码在工业界极化码在工业界5G标准中与标准中与Turbo码和码和LDPC码进行激烈竞争；码进行激烈竞争；2. 华为公司主推极化码进入华为公司主推极化码进入5G

24、。见提案！自己近期工作介绍：极化速率自己近期工作介绍：极化速率2009，E. Arikan and I. E. Telatar, On the rate of channel polarization, in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Seoul, Korea, Jun./Jul. 2009, pp. 1493-1495.高维核矩阵高维核矩阵2010, S. B. Korada, E. Sasoglu, and R. Urbanke, Polar codes: Characterization of exponent, bounds,

25、and constructions, IEEE Trans. Inf. Theory, vol. 56, no. 12, pp. 6253-6264, Dec. 2010.高维核矩阵有着更大的极化速率，也应当有着更优译码纠错性能。高维核矩阵设计高维核矩阵设计2015, N. Presman, O. Shapira, S. Litsyn, T. Etzion, and A. Vardy, Binary polarization kernels from code decompositions, IEEE Trans. Inf. Theory, vol. 61, no. 5, pp. 2227-2239, May. 2015.2015, H. Lin, S. Lin, S. Litsyn, and K. A. S. Abdel-Ghaffar, Linear and nonlinear binary kernels of polar codes of small dimensions with maximum exponents, IEEE Trans. Inf. Theory, vol. 61, n