Emmanuel Abbé and Colin Sandon receive IEEE Award

Emmanuel Abbé and Colin Sandon. Credit: EPFL

Emmanuel Abbé and Colin Sandon. Credit: EPFL

Professor Emmanuel Abbé at EPFL has been awarded the 2025 IEEE Information Theory Society Paper Award with Dr Colin Sandon for settling a conjecture on error-correcting codes dating back to the 1960s. 

The IEEE Information Theory Society Paper Award, presented by the IEEE Information Theory Society, honors exceptional contributions to the field of information theory. The Society is a leading international community in the science of information and has played a key role in advancing research on the mathematical underpinnings of data transmission, storage, and processing.

Each year, the award spotlights a paper published in the previous six years that has made a significant impact on the discipline. This year, the Award was given to Professor Emmanual Abbé (EPFL) and Dr Colin Sandon (now at EPFL) for their 2023 paper“A proof that Reed-Muller codes achieve Shannon capacity on symmetric channels”.

The paper presents a breakthrough in coding theory, a field of mathematics that deals with the efficient encoding of data for error protection.

About the paper

In 1948, the mathematician Claude Shannon showed that there's a maximum rate at which information can be transmitted over a channel without errors. But what wasn't clear was if there were codes that could actually achieve this maximum rate.

In their awarded paper, Abbé and Sandon present a new mathematical proof showing that a type of code called “Reed-Muller” can indeed achieve the maximum possible rate for transmitting information over a channel, known as the Shannon capacity.

While earlier work had achieved the first milestone for the special case of the “erasure” channels, with the work of Prof. Urbanke at EPFL, the toughest challenge was to show Reed-Muller codes also achieved capacity for more difficult channels that allow for “errors” (corruptions of the codewords coordinates that are not detectable). The main difficulty was finding a proof that worked even when previous mathematical shortcuts based on Bourgain-Friedgut’s sharp threshold theorems did not apply.

Abbé's and Sandon's breakthrough uses a new technique called “recursive boosting,” which decodes information by analyzing self-similar structures within the code. They also rely on combinatorial structures known as Sunflower set sytems, studied by Erdős in the 1960s. The findings settle this long-standing problem in coding theory and also have important implications for the security of communication channels (e.g., wire-tap secrecy) and quantum channels.

A recent paper by the authors and Maryna Viazovska from EPFL has also established further fascinating connections between this problem and a recent result of combinatorial number theory.

Author: Nik Papageorgiou

Source: Basic Sciences | SB

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