What Are the Ten Mathematical Challenges Shaping the Post‑Shannon Era?

Ten Mathematical Challenges for the Post‑Shannon Era

Seventy years after Claude Shannon’s seminal work, the communication industry still relies heavily on fundamental mathematics. Huawei’s board member and strategic research institute director Xu Wenwei recently presented ten mathematical challenges that the post‑Shannon information industry must address.

Huawei has established mathematics research institutes in Russia and France and collaborates with leading Chinese mathematicians such as Academics Zhang Pingwen, Xu Zongben, and Li Anmin, forming joint laboratories to drive theoretical advances.

These challenges define the transition to an intelligent society where everything is sensed, connected, and automated, demanding new mathematical breakthroughs.

Challenge 1: Lossy compression limit (semantic information theory).

Challenge 2: Breakthrough in source coding theory to reach lossless source compression limits.

Challenge 3: Fundamental service model for networks.

Challenge 4: Massive MIMO capacity domain.

Challenge 5: Non‑linear channel compensation.

Challenge 6: Optimal control of large‑scale communication networks.

Challenge 7: High‑precision fast solutions for inverse problems.

Challenge 8: High‑performance algebraic‑geometry (AG) error‑correcting codes.

Challenge 9: Interpretability of deep neural networks (DNN).

Challenge 10: Approximate computation of network‑level traffic matrices.