New Converses for the Relay Channel via Reverse Hypercontractivity

Jingbo Liu, Ayfer Özgür

Abstract: We revisit the primitive relay channel, introduced by Cover in 1987. Previously, the cut-set bound was shown to be loose for the primitive relay channel, in the discrete memoryless and the Gaussian cases, using the concentration of measure. In this paper, we give simpler proofs using reverse hypercontractivity, with shaper bounds and applying to wider range of channels. To our knowledge, this is the first application of reverse hypercontractivity in first-order converses in network information theory.