Upper bounds on the capacity of symmetric primitive relay channels

Consider a symmetric primitive relay channel, where, the source X wants to send information to the destination Y with the help of a relay Z, the relay Z can communicate to the destination Y via an error-free digital link of rate R₀, and Y, Z are conditionally independent and identically distributed given X. This paper presents two new upper bounds on the capacity of such relay channels, where the first one is a sharpened version of the recently proposed bound by (Xue, 2014), and the second one is novel. These two bounds are shown to be generally tighter than the cut-set bound, and as an example they are numerically evaluated for the case of binary symmetric channels.