CIF: Medium: Polar Coding for Data Storage: Theory and Applications

在我们现在生活的信息时代，对数字数据的可靠传输和存储的需求是至关重要的。使这种可靠传输和存储成为可能的是纠错码，它首先是由Claude Shannon在50多年前提出的。信道极化现象的发现和极化编码的相关发明，毫无疑问，这是近十年来纠错码理论中最具原创性和最深刻的发展之一。极化码可证明实现任何无记忆对称信道的容量，具有低编码和解码复杂度，从而为Claude Shannon在1948年提出的问题提供了第一个建设性解决方案。这一显著的结果引起了人们对在实践中利用极化编码潜力的极大兴趣。该项目的目标是推进极化码的理论，并使这些码更接近数据存储的实践。因此，研究人员不仅研究极化码的某些理论方面，而且还研究它们在VLSI电路中的实现以及它们在数据存储技术中的结合。鉴于从消费电子到海量数据仓库的应用对可靠、大容量数据存储的需求日益增长，本研究具有重大的经济和社会影响潜力，本项目解决了与信道极化、极化码设计方法和极化码解码算法性能相关的一些基本问题。具体而言，审议的问题包括： (1)各种通道的极化速度和极化核; (2)极化码列表译码算法的性能分析 (3)将极化码集成到联合检测和解码中 磁记录通道的结构; (4)固态存储器的非二进制极化码设计 非对称错误和重写约束; (5)极化编码技术在高速、高速、低噪声环境中的实现 这些具有挑战性的问题的解决需要新的方法和思想之间的接口信息理论和编码。了解数据存储系统的极化编码架构对广泛的通信信道有影响。这项研究的结果也与其他科学学科和工程技术有关，这些学科和技术正在被极化现象所彻底改变，包括信源编码，安全通信，网络信息理论，随机性提取和压缩感知。另一方面，硬件实现促进了算法发明和VLSI设计之间的相互作用，推动了电路技术的前沿。此外，该项目还为研究生提供了一个从事多学科研究并与数据存储行业合作伙伴互动的绝佳机会。

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 discovery of the channel polarization phenomenon and the associated invention of polar coding is, without doubt, one of the most original and profound developments 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 constructive solution to the problem posed by Claude Shannon in 1948. This remarkable result has engendered enormous interest in harnessing the potential of polar coding in practice. The objective of this project is to advance the theory of polar codes and to bring these codes much closer to the practice of data storage. Thus the investigators study not only certain theoretical aspects of polar codes, but also their implementation in VLSI circuits and their incorporation in data-storage technologies. In view of the increasing demand for reliable, high-capacity data storage, driven by applications ranging from consumer electronics to massive data warehouses, this research has significant potential for economic and societal impact.The present project addresses a number of fundamental problems related to channel polarization, polar code design methods, and performance of polar decoding algorithms. Specifically, the problems considered include the following: (1) Polarization speed and polarization kernels for a variety of channels; (2) Performance analysis of list-decoding algorithms for polar codes; (3) Integration of polar codes into joint detection and decoding architectures for magnetic recording channels; (4) Design of non-binary polar codes for solid-state memories with asymmetric errors and rewriting constraints; (5) Realization of polar coding technology in high-speed, low-power VLSI circuit implementations.The resolution of these challenging problems requires new methods and ideas on the interface between information theory and coding. Understanding polar coding architectures for data-storage systems has implications for a broad range of communication channels. The results of this research are also relevant to other scientific disciplines and engineering technologies that are being revolutionized by the polarization phenomenon, including source coding, secure communications, network information theory, randomness extraction, and compressive sensing. On the other hand, hardware implementation fosters an interplay between algorithmic invention and VLSI design, pushing the frontiers of circuit technology. The project furthermore provides an excellent opportunity for graduate students to engage in multi-disciplinary research and to interact with partners in the data-storage industry.