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

数字通信在我们的日常生活中无处不在，而数字存储设备已经成为保存我们信息的主要手段。在我们现在生活的“信息时代”，对可靠传输和存储数字数据的需求是至关重要的。使这种可靠的传输和存储成为可能的是纠错码，这是克劳德·香农在50多年前首先构想出来的。最近极性码的发明无疑是近十年来纠错码理论中最具原创性和最深刻的发展。极性码可证明地达到任何无内存对称信道的容量，具有低编码和解码复杂性，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，极性代码在实践中的影响是微不足道的。该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接近实践。如果成功，这项研究的结果很可能成为商业和国家安全领域众多通信应用的使能技术。为了使极码实用，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。本项目旨在开发一种线性时间构造算法，并明确保证其输出质量。研究人员还研究了极性码的代数和组合结构，目的是对信道极化率进行良好的分析处理。目前可用的经验结果表明，通道极化速率对于许多应用来说太慢了。因此，研究人员打算通过在连续抵消解码算法中引入某些关键修改，在短码到中等码长的情况下大幅提高极性码的性能。在这方面，一个特别有前途的想法是列表解码。本文致力于分析极性码的列表解码算法。此外，还研究了在高速低功耗VLSI中完整实现这种解码算法的方法。这部分的研究涉及解码器关键步骤的算法转换、有效的高吞吐量设计技术、仔细的VLSI复杂度/面积分析以及新的计算调度思想。最后，考虑了极性码和信道极化在点对点通信之外的应用。这些应用包括多址通道、中继通道、睡狼编码和信息论安全。

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.