Berger-Tung problem: A systematic approach based on canonical description

Even after three decades of research, the Berger-Tung problem remains open. The usual method attempts to identify the eponymous inner and outer bounds, tacitly bypassing the natural reference of the unwieldy operational definition. In this context, we show that the inner and outer bounds sometimes differ, making the usual approach untenable. As an alternative, we axiomatically reformulate the problem using our canonical description. In this framework, the Berger-Tung conjecture holds if and only if certain structural constraints have no impact on higher-order inner bounds. In parallel, we also lay down a roadmap towards computability that requires bounding of the gap between inner bounds of arbitrary order and the achievable region. As a first step, we consider partial side information problem, a specialization of the Berger-Tung problem, and bound the first-order gap in terms of Zamir´ s minimax noise capacity.