Tightness of Marton’s inner bound for broadcast channels

For a finite two-receiver discrete memoryless broadcast channel T, is Marton’s one-letter region always capacity-optimal? The counterexample target is strict superadditivity M(T⊗2)>2M(T), with a certified positive gap.

Why it matters and what counts as progress

Why it matters: It asks whether coding across two channel uses can outperform the best one-letter Marton quantity for one fixed finite channel.

What counts as progress: A finite broadcast channel with a certified strict two-letter Marton improvement, or a single-letter optimality theorem for a restricted channel class.

How the problem developed

1979 · Inner bound [1]
Katalin Marton Introduced the achievable inner bound for the discrete memoryless broadcast channel; whether it always equals capacity remained open.
20 Aug 2026 · Counterexample [2]
Mian Huang, Yanxiao Liu and Yi Liu Reported finite two-receiver discrete memoryless broadcast channels whose capacity region is strictly larger than Marton’s inner bound.

AI contribution

Sub-optimality of Marton's Inner Bound for the Two-Receiver Broadcast Channel

Mian Huang, Yanxiao Liu, Yi Liu

Huang, Liu and Liu give a finite two-receiver discrete memoryless broadcast channel T for which Marton’s two-use sum-rate quantity M(T⊗2) exceeds twice its one-use value M(T), with a certified gap above 1.8821×10⁻⁶ nats. Its one-letter Marton region is therefore strictly smaller than capacity.

AI involvementAI-centered

ImportanceMajor

Technical verificationFormal (exact rational arithmetic with outward-rounded MPFR interval certificates + human)

Human understandingFull