CIF: Small: Polar Codes --- From Theory to Practice

CIF：小码：Polar 码 --- 从理论到实践

• 批准号: 1116820
• 负责人: Alexander Vardy
• 金额: $ 49.46万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1116820&HistoricalAwards=false
• 关键词: CIF; Small; Polar; Codes; Theory

Digital communication pervades our daily lives while digital storage devices have become the principal means of preserving our information. During the "information age," in which we now live, the need for reliable transmission and storage of digital data is of paramount importance. What makes such reliable transmission and storage possible are error- correcting codes, first conceived by Claude Shannon over 50 years ago. The recent invention of polar codes is, without doubt, the most original and profound development in the theory of error-correcting codes in the past decade. Polar codes provably achieve the capacity of any memoryless symmetric channel, with low encoding and decoding complexity, thereby providing the first deterministic and constructive solution to the problem posed by Shannon in 1948. Nevertheless, the impact of polar codes in practice has been, so far, negligible. The objective of this project is to advance the theory of polar codes on one hand, and to bring polar codes much closer to practice on the other hand. If successful, the outcome of this research is likely to become an enabling technology for numerous communications applications, both commercial and for national security.In order to make polar codes practical, major obstacles must be resolved. The first key problem in the field is how to efficiently construct polar codes. This project aims to develop a linear-time construction algorithm, with explicit guarantees on the quality of its output. The investigators also study algebraic and combinatorial structure of polar codes, with the goal of developing a good analytical handle on the rate of channel polarization. Currently available empirical results indicate that the rate of channel polarization is too slow for many applications. Thus the investigators intend to drastically improve the performance of polar codes, at short to moderate code lengths, by introducing certain key modifications in the successive-cancellation decoding algorithm. One especially promising idea in this regard is list decoding. A concerted effort is devoted to the analysis of list decoding algorithms for polar codes. Furthermore, a full implementation of such decoding algorithms in high-speed and low-power VLSI is pursued. This part of the research involves algorithmic transformations for the key steps of the decoder, effective high-throughput design techniques, careful VLSI complexity/area analysis, and new computation scheduling ideas. Finally, applications of polar codes and channel polarization beyond point-to-point communications are considered. Such applications include multiple-access channels, relay channels, Slepian-Wolf coding, and information-theoretic security.

数字通信渗透到我们的日常生活中，而数字存储设备已经成为保存我们信息的主要手段。在我们现在所处的“信息时代”，对数字数据的可靠传输和存储的需求至关重要。使这种可靠的传输和存储成为可能的是纠错码，它最初是由克劳德·香农在50多年前构思的。毫无疑问，最近极性码的发明是近十年来纠错码理论中最具原创性和最深刻的发展。极性码可以以较低的编码和译码复杂度达到任何无记忆对称信道的容量，从而为香农在1948年提出的问题提供了第一个确定性和建设性的解决方案。然而，到目前为止，极地代码在实践中的影响可以忽略不计。本项目的目标是一方面推进极性码的理论，另一方面使极性码更加贴近实际。如果成功，这项研究的结果很可能成为许多通信应用的使能技术，无论是商业应用还是国家安全应用。要使极地码实用，必须解决主要障碍。该领域的第一个关键问题是如何有效地构造极性码。该项目旨在开发一种线性时间构造算法，并明确保证其输出的质量。研究人员还研究了极化码的代数和组合结构，目的是开发一个很好的信道极化速率的分析处理。目前已有的实验结果表明，对于许多应用来说，信道极化速率太慢。因此，研究人员打算通过在连续消除译码算法中引入某些关键修改来显著改善短到中等码长的极性码的性能。在这方面，一个特别有希望的想法是列表解码。本文对极性码的列表译码算法进行了分析。并在高速低功耗的VLSI中实现了这种译码算法。这一部分的研究涉及解码器关键步骤的算法转换、有效的高通量设计技术、仔细的VLSI复杂度/面积分析以及新的计算调度思想。最后，讨论了极化码和信道极化在点对点通信之外的应用。这些应用包括多址信道、中继信道、Slepian-Wolf编码和信息论安全。