Tom Dean


Tom Dean
PhD Candidate
Department of Electrical Engineering
Stanford University
Advisor: Professor Andrea Goldsmith
Group: Wireless Systems Lab

Packard 340
350 Serra Mall
Stanford, CA



I am broadly interested in the intersection of complexity theory, cryptography, information theory and mathematical optimization. The majority of my research is on the decoding of Multiple-Input Multiple-Output (MIMO) wireless signals. MIMO wireless systems utilize multiple antennas at both the transmitter and receiver to allow users to spatially multiplex data and leverage spatial diversity, thereby increasing throughput and reliability. MIMO systems are nearly ubiquitous today and appear almost any modern wireless product as they are integral parts of both the WiFi and LTE standards. Performing accurate decoding of MIMO signals is known to be a computationally difficult task and is the subject of a large body of research. I have found studying MIMO decoding to be an incredibly wealthy avenue to explore fundamental problems in mathematics and computer science while simultaneously providing practical solutions to real-world problems.

Notable Projects

Physical Layer Cryptography through Massive MIMO

We have shown that under proper conditions, MIMO decoding is computationally equivalent to solving certain lattice problems. Namely, decoding is at least as hard as solving the same lattice problems that underpin the security of Learning With Errors (LWE) based cryptographic constructions. LWE-based constructions are currently leading candidates to provide cryptographic security in the presence of quantum computing. We have further used this reduction to show that two users can communicate securely over a MIMO channel in the presence of an eavesdropper without the use of a key. Our proposed scheme achieves CCA security with almost no computational or information overhead. Our scheme creates a communications channel where cryptographic security is an inherent part of the channel. Because the underlying reduction is related to lattice problems, the transmitted information remains inaccessible from a computational perspective even provided the existence of quantum computation.

Blind MIMO Decoding

My recent work has focused on blind decoding of MIMO signals; that is, estimating transmitted symbols with zero prior knowledge of either the channel state information (CSI) or the underlying data. This has long been assumed to be a complex problem. Modern wireless systems dedicate many resources to accurately measure CSI to support (non-blind) decoding. We have recently shown in that we can efficiently and reliably perform blind decoding by posing the problem of decoding symbols from an unknown MIMO channel as a non-convex geometric optimization problem. The problem is equivalent to fitting a minimum volume parallelepiped to a set of observed samples. We leverage techniques from mix-integer and linear programming to efficiently solve this non-convex problem. The performance of our scheme at low dimensions (roughly, ) rivals current methods for decoding when CSI is known, in both time complexity and error performance. This result has the potential to be highly impactful in the design of future generations of wireless systems. At high dimensions, our blind decoding algorithm has, in the worst case, exponential time complexity. In fact, we show that the blind decoding problem is computationally equivalent to the Hadamard Maximal Determinant problem, a famous open problem in mathematics. This result is interesting for several reasons. First, we believe that we have a very powerful algorithm for finding large maximum-determinant matrices. Beyond addressing fundamental questions in mathematics, being able to find large Hadamard matrices may have practical implications for coding theory and statistical estimation. Additionally, at high dimensions, the problem of finding Hadamard matrices is believed to be extremely difficult from a computational perspective. Thus, our result suggests that blind decoding may be computationally prohibitive in massive MIMO systems.


Journal publications

Talks/posters/conference publications