Study on polar transformation and channel models as fundamental principles of polar codes

• Project/Area Number: 17K06422
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Communication/Network engineering
• Research Institution: University of Fukui
• Principal Investigator: Iwata Ken-ichi 福井大学, 学術研究院工学系部門, 准教授 (80284313)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Project Status: Completed (Fiscal Year 2020)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2017: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
• Keywords: polar符号 / ポーラ符号 / 情報理論 / 通信路符号 / 通信路モデル / polar変換 / 符号理論

Outline of Final Research Achievements

Arikan proposed polar codes in 2008. This research investigated the following study subjects (1) to (3) concerning the polar transform, which is the basic principle of polar codes: (1) performance evaluation of channel model with the multiple-input by conditional Renyi entropy, (2) generalization of the quantization algorithm for the channel model used in the polar transform, and (3) multilevel channel polarization for generalized erasure channels.

Academic Significance and Societal Importance of the Research Achievements

polar変換における通信路モデ ルの近似アルゴリズムに関して幾つかの研究成果がある．これらの研究成果は，polar符号を構成する場合における情報点の選択に関して役立つと考える．また，一般化消失通信路に対する多段分極に関する研究成果は，多元ポーラ符号の多段分極現象に関して，与えられた通信路が消失通信路を一般化した通信路モデルの場合の漸近分布解析を解明しており，今後の研究発展一つの礎を与えたと考える．polar符号は，第5世代移動体通信（5G）に用いられており，今後の発展が期待される符号である．

Research Products

• [Journal Article] Modular Arithmetic Erasure Channels and Their Multilevel Channel Polarization (2020)
  • Author(s): Sakai Yuta、Iwata Ken-Ichi、Fujisaki Hiroshi
  • Journal Title: IEEE Transactions on Information Theory Volume: 66 Issue: 7 Pages: 3976-4006
  • DOI: 10.1109/tit.2020.2996977
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Extremality Between Symmetric Capacity and Gallager’s Reliability Function $E_{0}$ for Ternary-Input Discrete Memoryless Channels (2018)
  • Author(s): Sakai Yuta、Iwata Ken-ichi
  • Journal Title: IEEE Transactions on Information Theory Volume: 64 Issue: 1 Pages: 163-191
  • DOI: 10.1109/tit.2017.2751500
  • Peer Reviewed
• [Presentation] Countably Infinite Multilevel Source Polarization for Non-Stationary Erasure Distributions (2019)
  • Author(s): Y. Sakai, K. Iwata, H. Fujisaki
  • Organizer: 2019 IEEE International Symposium on Information Theory
  • Int'l Joint Research
• [Presentation] Asymptotic Distribution of Multilevel Channel Polarization for a Certain Class of Erasure Channels (2018)
  • Author(s): Sakai Yuta、Iwata Ken-Ichi、Fujisaki Hiroshi
  • Organizer: Proceedings of 2018 IEEE International Symposium on Information Theory, DOI:10.1109/ISIT.2018.8437921
  • Int'l Joint Research
• [Presentation] Dynamic Programming Approach of Optimal Upgradation Algorithm for an Auxiliary Random Variable of a Bernoulli Random Variable (2018)
  • Author(s): Sakai Yuta、Iwata Ken-Ichi
  • Organizer: Proceedings of 2018 IEEE International Symposium on Information Theory, DOI:10.1109/ISIT.2018.8437693
  • Int'l Joint Research
• [Presentation] Concrete Examples of Countably Infinite Multilevel Source Polarization with a Certain Infinite Group (2018)
  • Author(s): Sakai Yuta、Iwata Ken-Ichi、Fujisaki Hiroshi
  • Organizer: 第41回情報理論とその応用シンポジウム
• [Presentation] Optimal quantization of B-DMCs maximizing α-mutual information with monge property (2017)
  • Author(s): Sakai Yuta、Iwata Ken-ichi
  • Organizer: 2017 IEEE International Symposium on Information Theory (ISIT2017)
  • Int'l Joint Research
• [Presentation] Sharp bounds on Arimoto's conditional Renyi entropies between two distinct orders (2017)
  • Author(s): Sakai Yuta、Iwata Ken-ichi
  • Organizer: 2017 IEEE International Symposium on Information Theory (ISIT2017)
  • Int'l Joint Research
• [Presentation] Asymptotic Distribution of Multilevel Channel Polarization for a Certain Class of Erasure Channels (2017)
  • Author(s): Yuta Sakai, Ken-ichi Iwata, Hiroshi Fujisaki
  • Organizer: 第40回情報理論とその応用シンポジウム予稿集
• [Presentation] Extremality for Arimoto’s conditional Renyi entropy and error exponents of Gallager’s form (2017)
  • Author(s): Yuta Sakai, Ken-ichi Iwata
  • Organizer: 第10回シャノン理論ワークショップ予稿集
• [Remarks] Sharp Bounds on Arimoto's Conditional ...
  • URL: https://arxiv.org/abs/1702.00014
• [Remarks] Asymptotic Distribution of Multilevel Channel ...
  • URL: https://arxiv.org/abs/1801.04422