Universally optimal (wiretap) codes
2026-08-10 • Information Theory
Information Theory
AI summaryⓘ
The authors Cohn, Kumar, and Zhao previously studied special sets of codes called universally optimal (UO) codes that are very good at minimizing 'energy' in certain mathematical settings. In this work, the authors show that these UO codes also work best for a specific information theory problem involving wiretap channels, which are communication systems where an eavesdropper tries to listen in. Specifically, the authors prove UO codes maximize a measure called α-mutual information (with α=2) when the main communication channel has no noise. This means UO codes are the best choice for sending secret messages securely in this scenario.
Universally Optimal CodesEnergy Minimizationα-Mutual InformationWiretap ChannelNoiseless ChannelInformation TheoryCode OptimizationSecure Communication
Authors
Madhura Pathegama, Alexander Barg
Abstract
Universally optimal (UO) codes were introduced by H. Cohn and A. Kumar in 2007 and later extended to the discrete setting by Cohn and Y. Zhao. They minimize the ``energy'' among all codes of the same size for a certain class of potential functions. So far only a small number of specific functionals have been linked to information theory problems. We add one more, showing that UO codes optimize $α$-mutual information for $α=2$ in the context of wiretap channels with a noiseless main channel. This implies that UO codes are optimal for transmission over this type of wiretap channels.