Since the first mobile phones became available in the 1980s, four distinct "generations" of wireless networks have been deployed to support reliable transmission of ever-increasing volumes of data to a growing number of users. What makes such reliable transmission of information possible are error-correcting codes, first conceived by Claude Shannon over 60 years ago. Polar coding is a key new error-correction technology introduced in the fifth wireless generation, known as 5G, that is currently being developed and standardized. Thus, soon enough, consumers the world over will all be using polar codes whenever making a phone call or accessing the Internet on a mobile device. Polar codes provably achieve the fundamental limits of communication established by Shannon in 1948, with low encoding and decoding complexity. Nevertheless, numerous challenges must be overcome in order to realize the full potential of polar coding in wireless communications. This project addresses these challenges to facilitate successful deployment of polar codes in 5G systems, while investigating fundamental problems in polar coding that lie beyond the 5G time horizon. These problems include polarization for time-varying channels and polar coding for channels with deletions. The results from this part of the investigation will contribute to the foundations of error-correction coding theory, and will also have an impact on adjacent scientific disciplines that are influenced by the polar-coding paradigm.
The discovery of channel polarization and polar codes is universally recognized as an historic breakthrough in coding theory. For short block lengths, polar codes under cyclic-redundancy-check-aided successive-cancellation list decoding are currently the best known coding scheme for binary-input Gaussian channels. Due to this and other considerations, 3GPP has decided to incorporate polar codes in the 5G wireless communications standard. The overarching goal in this project is to explore new frontiers in polar coding, thereby fundamentally advancing the current state-of-the-art in the field. Part of the research aims for immediately relevance to successful deployment of polar codes in 5G, whereas other parts focus on key theoretical problems in polar coding that lie beyond the 5G time-horizon. The specific objectives in this project are as follows: (1) Attain the gains of cyclic-redundancy-check-aided polar list-decoding with significantly lower complexity; (2) Construct practical universal polar codes that are not channel-dependent and provide near-optimal finite-length performance; (3) Develop code-domain multiple access techniques based on polar codes to enable massive connectivity; (4) Design and evaluate polar coding schemes for extended classes of channels, going well beyond the original memoryless and stationary set-up; (5) Extend the polarization paradigm and design polar codes for channels with deletions; (6) Develop a full-scale efficient, low-latency, and low-power system-on-chip implementation of polar list decoders. This project is a natural outgrowth of extensive and transformative prior work carried out by the investigators in polar coding.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
