Plenary Talks

Calderbank-Shor-Steane (CSS) codes are quantum codes constructed from a pair of nested classical codes \(C_2 \subseteq C_1\). The choice of the nested code pair \((C_1,C_2)\) has a major influence on the properties of the resulting CSS code. One should of course choose \((C_1,C_2)\) so that the resulting CSS code has good parameters --- blocklength, dimension, and minimum distance. But, to be useful for quantum computing applications, it is important that the CSS code admit fault-tolerant physical implementations of desired logical actions (quantum gates) on the code space. For example, an important open problem in this context is the construction of asymptotically good CSS codes that admit transversal physical realizations of logical T gates.

In this talk, we present an approach to characterize pairs \((C_1,C_2)\) such that the resulting CSS code admits a targeted logical action via transversal physical Z-rotations. Specifically, the targeted logical action can be any given (logical) diagonal gate acting on the logical qubits, for example, the logical T gates mentioned in the open problem above. We also illustrate how \((C_1,C_2)\) pairs can be constructed to meet the conditions in our characterization. We outline the strengths and limitations of our approach when compared to other related work.

The talk is based on joint work with K. Sai Mineesh Reddy.

Navin Kashyap is a Professor in the Department of Electrical Communication Engineering at the Indian Institute of Science (IISc), Bangalore. Prior to joining IISc in 2011, he was on the faculty of the Department of Mathematics and Statistics at Queen's University, Kingston, Ontario, Canada. His research interests lie primarily in the application of algebraic, combinatorial and probabilistic methods in information and coding theory. Prof. Kashyap is a past recipient of the Swarnajayanti Fellowship awarded by the Department of Science and Technology, Government of India.

Transformer models have achieved remarkable empirical success through accurate next-token prediction and an ability to adapt in context from limited data. In this talk, I will show how these capabilities offer a new lens on canonical problems in information theory, and how in-context learning can be interpreted through classical ideas such as universal prediction. The focus will be on lossless compression and Estimation. I will first revisit lossless compression through the predict-then-code paradigm, showing that modern language models, when combined with arithmetic coding, can deliver striking performance. I will then discuss how large language models can be incorporated into the Slepian-Wolf framework for distributed compression. Finally, I will turn to wireless communications, casting symbol estimation as an in-context inference problem in which observations depend on unknown latent parameters. Recent results suggest that attention-based transformers can behave as adaptive estimators that implicitly approximate Bayesian inference. Taken together, these examples illustrate how transformer-based models can improve performance in classical problems in information and communication theory, especially in regimes where standard simplifying assumptions no longer hold.

Krishna R. Narayanan (Fellow, IEEE) received the Ph.D. degree in electrical engineering from Georgia Institute of Technology in 1998. Since 1998, he has been with the Department of Electrical and Computer Engineering, Texas A&M University, where he is currently the Sanchez Chair Professor. His current research interests include the design of massive uncoordinated multiple access schemes, coded distributed computing, and applications of machine learning to wireless communications. He was elected as a fellow of IEEE for contributions to coding for wireless communications and data storage. He received the 2022 IEEE Joint Communications Society and Information Theory Society Best Paper Award. He also the received the 2006 and 2020 Best Paper Awards from the IEEE Technical Committee for Signal Processing for Data Storage. He served as an Associate Editor for coding techniques for IEEE Transactions on Information Theory and an Area Editor (and an Editor) for the coding theory and applications area for IEEE Transactions on Communications.

In this talk, I will present my journey in high-dimensional sparse systems. The ultimate goal is the minimum mean-square error (MMSE) recovery of sparse signals from minimum necessary measurements. The starting point was analysis of the MMSE performance in high-dimensional limit via the replica method -- a non-rigorous tool in statistical physics. My interest shifted from non-rigorous analysis to rigorous analysis -- state evolution for analyzing message-passing (MP) algorithms that can potentially achieve the MMSE performance. Using state evolution, I am now pioneering two new worlds from the initial world in high-dimensional systems: long-memory MP and sublinear MP.

Keigo Takeuchi received the B.Eng., M.Inf., and Ph.D. degrees in informatics from Kyoto University, Kyoto, Japan, in 2004, 2006, and 2009, respectively. From 2009 to 2016, he was an Assistant Professor with the Department of Communication Engineering and Informatics, The University of Electro-Communications, Tokyo, Japan. He held visiting appointments at the Norwegian University of Science and Technology (NTNU), Norway, and National Sun Yat-sen University (NSYSU), Taiwan. He is currently an Associate Professor with the Department of Electrical and Electronic Information Engineering, Toyohashi University of Technology, Aichi, Japan. His current research interests include wireless communications, statistical signal processing, and statistical-mechanical informatics.