New Frontiers in Coding Theory: Reed-Muller and Polar Codes

编码理论的新前沿：Reed-Muller 和 Polar 码

基本信息

批准号：
RGPIN-2019-05448
负责人：
Wang, Lele
金额：
$ 2.77万
依托单位：
University of British Columbia
依托单位国家：
加拿大
项目类别：
Discovery Grants Program - Individual
财政年份：
2021
资助国家：
加拿大
起止时间：
2021-01-01 至 2022-12-31
项目状态：
已结题

来源：
https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=738278
关键词：
New Frontiers Coding Theory Reed

项目摘要

Coding theory is an important bridge between information theory, which studies the fundamental limits of data transmission, and practical systems, which require low-complexity computationally efficient algorithms. This research program investigates fundamental theories as well as practical designs of two closely related families of codes---Reed-Muller codes and polar codes. On the theory side, we plan to attack the long-standing conjecture that Reed-Muller codes are capacity achieving under maximum a posteriori decoding over binary memoryless symmetric channels. We will perceive Reed-Muller codes from a channel polarization perspective and build on the exciting progress by Kudekar, Kumar, Modelli, Pfister, Sasoglu, and Urbanke, who established optimality of the code over the special case of binary erasure channels. On the practical side, we plan to investigate the recently invented polar codes, which have been adopted in the newly released 5G NR (New Radio) standard. First, we aim to improve the finite-length performance of polar codes by incorporating ideas from Peres's random-bit generator. Second, we plan to explore the polarization principle in new applications beyond point-to-point communication, such as multi-user communication in wireless networks, distributed compression in emerging data storage systems, caching techniques for content delivery networks, sensing matrix design for group testing, among others.

编码理论是信息理论之间的重要桥梁，它研究了数据传输的基本限制和需要低复杂性计算有效算法的实用系统。该研究计划调查了两个密切相关的代码系列的基本理论以及实用设计 - 芦苇刺激法规和极地代码。从理论方面来说，我们计划攻击长期以来的概念，即在最大的后验分解中，在二进制无内存的对称通道上，芦苇毛刺代码的能力达到了最大的能力。我们将从频道两极分化的角度来感知芦苇 - 穆勒代码，并建立在Kudekar，Kumar，Modelli，Pfister，Sasoglu和Urbank的令人兴奋的进度上，后者在二元擦除频道的特殊情况下确立了代码的最佳性。在实用方面，我们计划研究最近发明的极地代码，这些代码已在新发布的5G NR（新广播）标准中采用。首先，我们旨在通过编码佩雷斯随机生成器的想法来提高极地代码的有限长度性能。其次，我们计划探索超出点对点通信以外的新应用程序中的两极分化原理，例如无线网络中的多用户通信，新兴数据存储系统中的分布式压缩，用于内容交付网络的缓存技术，感应用于组测试的矩阵设计等。