信道极化和极化码版本2针对学生ppt课件.ppt

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1、极化码(Polar codes),达到信道容量的编码方案,黄志亮,讨论组安排,赵頔汪宇左德遥张施怡,基本要求：做ppt外行也能明白讨论前一到两天把ppt发给所有人,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,The Road to Channel Capacity,信道极化和极化码,代表文章： Erdal Arikan, Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Sym

2、metric 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 for an invention that answe

3、rs 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. We congratulate Prof. Erdal Arkan who received th

4、e 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（Polar Codes）,信息论和编码领域顶级期刊(IEEE T

5、rans 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,Erdal Arikan和我,信道：概率模型 - 达到容量一,信道：信道举例 - 达到容量二,信道编码定理 - 达到容量三,码率：R = K/N，误码率：Pe,信道容量：C=maxp(x)I(X;Y)（bits per transmission）（二进制输入）信道编码定理： 无差错传输条件下（Pe=0），最大可达码率为C,Eb/N0=0.188dB，C=0.5：Eb/N0=0.188dB的BiAWGN信道，无差错传输条件下，无论如何设计编码器和译码器， R最大只能到0.5。,汉明码LDP

6、C码极化码,LDPC码性能展示- 达到容量四,From paper: Yu Kou, Shu Lin, “Low-Density Parity-Check Codes Based on finite geometries： A Rediscovery and New Results”, IEEE Trans. Infor. Theory, Vol 47, No 7, Nov 2001,极化码- 达到容量五,From paper: Erdal Arikan, Channel Polarization: A Method for Constructing Capacity-Achieving Co

7、des for Symmetric Binary-Input Memoryless Channels, IEEE Trans. on Information Theory, vol. 55, 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

8、相当或更好的性能。,From paper: Ido Tal and Alexander Vardy, “List Decoding of Polar codes”, IEEE Trans. Infor. Theory, Vol 61, No 5, May 2015.,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.

9、K. Niu and K. Chen, “Stack decoding of polar codes,” Electron. Lett., vol. 48, no. 12, 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 decod

10、ing of polar codes,” IEEE Trans. Commun., vol. 61, no. 8, pp. 3100-3106, Aug. 2013.“Beyond turbo codes: Rate-compatible puntured polar codes.” ICC 2013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,（2）南京邮电大学Polar lattices: where Arikan meets Forney. ISIT 2013On the analysis of multiplicative-

11、repetition codes and polar codes over binary erasure channels. WCSP 2012Cooperative 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

12、 channel. 2012 ICCSNTDesigns of Bhattacharyya parameter in the construction of polar codes. 2011 WiCOM,极化码研究现状：国内研究,（3）中南大学A novel channel polarization on binary discrete memoryless channels. 2010 ICCS,（4）北京航空航天大学A novel rate-adaptive distributed source coding scheme using polar codes. 2013, Communi

13、cations Letters, IEEE,（5）浙江大学On the polar codes for MIMO. WCSP 2013Polar 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,（7）浙江师范大学Z.L. Huang, C.J. Diao and M.

14、 Chen, “Latency Reduced Method for Modified 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

15、 for Polar Codes”，IEEE Communications Letters. 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，2013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：国外研究2,EPFL：

16、洛桑联邦理工学院 瑞士RdigerUrbanke: 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 we

17、ll as the 2014 IEEE 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,

18、2010S. B. Korada, PHD Thesis: Polar codes for channel and source coding.,极化码研究现状：国外研究3,Emre 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,” i

19、n Proc. 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. R. Pedarsani, S. H. Hassani, I. Tal, and E. Telatar, “On th

20、e construction 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：国外研究4,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 Trans. on Informat

21、ion 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,上次报告：2013年底 用IEEExpolare搜索”polar codes”一共有183篇 在arxiv.org上搜索”polar codes”一共有124篇 IEEE Trans. on

22、 Information Theory上一共15篇,本次报告：2016年9月 用IEEExpolare搜索”polar codes”一共有477篇 在arxiv.org上搜索”polar codes”一共有249篇 IEEE Trans. on Information Theory上一共37篇,极化码在工业界,5G标准中与Turbo码和LDPC码进行激烈竞争；,2. 华为公司主推极化码进入5G。,见提案！,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. I

23、EEE Int. Symp. Inf. Theory (ISIT), Seoul, Korea, Jun./Jul. 2009, pp. 1493-1495.,高维核矩阵,2010, S. B. Korada, E. Sasoglu, and R. Urbanke, Polar codes: Characterization of exponent, bounds, 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

24、。,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 pol

25、ar codes of small dimensions with maximum exponents, IEEE Trans. Inf. Theory, vol. 61, no. 10, pp. 5253-5270, Oct. 2015.,近年来，研究者们对高维核矩阵的设计进行了较充分的研究，已经有了不错的结果，如下面两篇文章。,但是，,高维核矩阵的研究存在一个瓶颈：其对应的连续消去译码算法的复杂度为O(2lNlogN)。,我近期的成果,当核矩阵维数l不大于16时，将SC译码复杂度从O(2lNlogN)降低为O(lNlogN)，也即使得高维核矩阵的研究走向实际。,结果让人激动： l=16时，

26、极化速率为0.518，只是稍微大于原l=2时的极化速率0.5，但是其译码纠错性能提高了0.5dB，甚至更多，这是非常大的一个提升，也是比较意外的一个结果。,仿真结果1: SC译码,仿真结果2： List SC译码,Fig .2. List SC decoding performance of polar codes with kernels G2 and G16. Their Block lengths are 256 and rates are 0.5. Codes are constructed using GaussianApproximation methods at Eb/N0=2dB. 28 is the polar code of kernel G2 with block length 256. 162 is the polar code of kernel G16 with block length 256. L=1 means List size is 1.,谢谢大家！,