Expanding and Deepning Probabilistic Method in Coding Theory

2015 Fiscal Year Final Research Report

• Project/Area Number: 25289114
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Communication/Network engineering
• Research Institution: Nagoya Institute of Technology
• Principal Investigator: Wadayama Tadashi 名古屋工業大学, 工学(系)研究科(研究院), 教授 (20275374)
• Co-Investigator(Kenkyū-buntansha): IZUMI Taisuke 名古屋工業大学, 大学院工学研究科, 准教授 (20432461) ; MIMURA Kazushi 広島市立大学, 情報科学研究科, 准教授 (40353297)
• Co-Investigator(Renkei-kenkyūsha): WATANABE Osamu 東京工業大学, 情報理工学研究科, 教授 (80158617) ; IWATA Kenichi 福井大学, 工学研究科, 准教授 (80284313) ; HAYASHI Kazunori 京都大学, 情報科学科, 准教授 (50346102)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 符号理論 / 情報理論 / 統計力学 / 理論計算機科学 / LDPC符号 / 疎グラフ / ランダムグラフ

Outline of Final Research Achievements

The goal of this project is to deepen and to expand modern coding theory with respect to probabilistic methods. The three main threads of the project consists of: (1) analysis on LDPC/LDGM codes based statistical mechanical methods (Mimura and Wadayama), (2) establishment of theory of non-linear observation systems based on sparse graphs, (3) sparse random graphs (Wadayama and Izumi). We have conducted corroborative research works and obtained some theoretical results. Some examples of our contributions are following: information theoretical analysis on group testing based sparse graphs, statistical mechanical analysis on non-linear codes based sparse graphs, several problems on random graphs, applications of Lovasz lemma, and communication complexity and its applications to distributed algorithms.

Free Research Field

符号理論