Fundamental study on theory and applications of channel polarization

信道极化理论与应用基础研究

• 批准号: 22560375
• 负责人: TANAKA Toshiyuki
• 金额: $ 2.75万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22560375/
• 关键词: 通信路分極; ポーラ符号; 通信路容量; 通信路符号化; 情報通信工学; 誤り訂正符号

Polar codes combined with successive-cancellation decoding, that were newly proposed in 2008, have been attracting attentions of researchers as error-correcting codes that have been proven to saturate the symmetric capacity for any memoryless channel in the limit of long codelength, while requiring relatively low computational complexity in encoding and decoding. In this research project, aiming at obtaining understandings that will be useful in constructing codes with better performance, we have elucidated the phenomenon of channel polarization, which lays the mathematical basis for high performance of polar codes. We have obtained a result on asymptotic decoding error probability in a coderate-dependent form, by refining existing asymptotic results on decoding error probability. We have also studied channel polarization over non-binary alphabet, and have obtained a necessary and sufficient condition for an invertible ?×? matrix on Fq to induce channel polarization.

2008年新提出的Polar码与逐次消除译码相结合的纠错码已被证明能够在长码长限制下使任何无记忆信道的对称容量饱和，同时需要相对编码和解码的计算复杂度低 在本研究项目中，为了获得有助于构建性能更好的代码的理解，我们阐明了信道极化现象，这奠定了基础。我们还研究了非二进制字母表上的信道极化，并通过改进现有的解码错误概率结果，得到了与码率相关的渐近解码错误概率的结果。获得了 Fq 上可逆 ?×? 矩阵引起通道极化的充要条件。

项目成果

Rate-Dependent Analysis of the Asymptotic Behavior of Channel Polarization

• DOI: 10.1109/tit.2012.2228295
• 发表时间: 2011-10
• 期刊: IEEE Transactions on Information Theory
• 影响因子: 2.5
• 作者: Seyed Hamed Hassani;R. Mori;Toshiyuki TANAKA;R. Urbanke

Chanel polarization on qary discrete memoryless channels by arbitrary kernels

任意内核在 qary 离散无记忆通道上的通道极化

• 发表时间: 2010
• 作者: R.Mori;T.Tanaka
• 通讯作者: T.Tanaka

ある確率的力学系,通信路分極とポーラ符号

随机动力系统、信道极化和极化码

• 发表时间: 2012
• 作者: S. H. Hassani;R. Mori;T. Tanaka;R. Urbanke;Toshiyuki TANAKA;田中利幸
• 通讯作者: 田中利幸

Channel polarization on q-ary discrete memoryless channels by arbitrary kernels

• DOI: 10.1109/isit.2010.5513568
• 发表时间: 2010-01
• 期刊: 2010 IEEE International Symposium on Information Theory
• 作者: R. Mori;Toshiyuki TANAKA

Non-binary polar codes using Reed-Solomon codes and algebraic geometry codes

• DOI: 10.1109/cig.2010.5592755
• 发表时间: 2010-07
• 期刊: 2010 IEEE Information Theory Workshop
• 作者: R. Mori;Toshiyuki TANAKA