Explicit Constructions of Lossless Expanders and Error-Correcting Codes
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zhang-rachelyz-phd-eecs-2026-thesis.pdf
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Author(s)
Zhang, Rachel Yun
Advisor(s)
Kalai, Yael Tauman
Vaikuntanathan, Vinod
Date Issued
May 2026
Publisher
Massachusetts Institute of Technology
Abstract
This thesis studies error-correction and robustness in modern settings. One of the main results in this thesis is the first explicit construction of two-sided lossless expanders. A lossless expander is a sparse graph where every small set of vertices has nearly as many neighbors as its sparsity permits. While a random graph is a lossless expander with high probability, constructing lossless expanders explicitly remained open for many years. We resolve this problem by identifying a connection to the relatively new area of high-dimensional expanders. Going beyond lossless expanders, we explore further applications of what we call “modern expanders” — expander constructions developed over the last two decades — to error-correcting codes. In particular, we obtain a simple, near-optimal construction of ε-balanced codes. The second part of this thesis studies the role of feedback in error-correcting codes. Feedback allows the sender to learn information about the receiver’s state throughout the communication process. Prior work established that noiseless feedback can significantly improve the error resilience of codes. We develop new feedback-based error-correcting codes that achieve the same performance using only minimal feedback, and we prove new bounds for list decoding. Additionally, we show for the first time that even noisy feedback can improve the error resilience of codes.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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