Capacity of the primitive diamond relay channel

Determine the capacity of the primitive diamond relay channel for general product-form broadcast channels with finite-capacity orthogonal relay-to-receiver links.

Background

The paper studies a primitive diamond relay channel in which a source communicates with two relays through a product-form memoryless broadcast channel, while each relay sends a finite-rate description to the destination over an orthogonal noiseless link. The paper derives a new single-letter outer bound and compares it with existing converse bounds and a decode–forward/compress–forward time-sharing inner bound.

Despite these bounds, the exact capacity is not established for the general channel. The unresolved gap between inner and outer bounds motivates continued work on sharper converses, including more refined auxiliary-receiver techniques discussed in the conclusion.