Achievable rates for the relay channel with orthogonal receiver components

This paper studies lower bounds on the capacity of the relay channel with orthogonal receiver components (also referred to as primitive relay channel). We show that the lower bound in Theorem 7 of Cover and El Gamal, which uses mixed decode-forward and compress-forward strategies, is identical to the lower bound of Chong, Motani and Garg, and is always larger than or equal to the recent lower bound of Mondelli, Hassani and Urbanke. We provide a simplified expression for the lower bound in Theorem 7 of Cover and El Gamal and interpret one of its auxiliary variables as implementing the randomized time-sharing strategy. Next, we compare the lower bound for the Gaussian relay channel with orthogonal receiver components to existing upper bounds. Finally, we disprove a conjecture by Ahlswede and Han on the capacity of the subclass of relay channels with orthogonal receiver components and i.i.d. output.