Exact reliability in the low-rate classical channel-coding regime

Characterize the exact reliability function for classical channel coding at communication rates below the critical rate, where the random-coding and sphere-packing bounds do not coincide.

Background

For classical channel coding with a fixed input distribution, the reliability function is bounded below by the random-coding exponent and above by the sphere-packing exponent. These bounds coincide in the high-rate regime but generally differ for rates below the critical rate. The paper identifies determining the exact reliability in this low-rate region as an unresolved problem that persists even for classical channels, thereby placing the quantum reliability results in the context of a broader longstanding limitation in coding theory.

References

Characterizing the exact reliability for the low-rate regime is a longstanding open problem even in the classical case.

— Universality Sacrifices Reliability in Classical-Quantum Channel Coding  (2610.01941 - Watanabe et al., 1 Oct 2026) in Section “Classical-quantum channel coding”