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.
