Capacity of less noisy relay channels

In this paper, we characterize the capacity of two new classes of relay channels, which we call more capable and less noisy relay channels. In these relay channels, the channel seen by the relay is stronger than that seen by the destination in a certain sense, which resembles the conditions for the more capable and less noisy broadcast channels. In more capable relay channels, decode-and-forward (DF) is shown to be optimal. The more capable relay channel includes as special cases several examples in the literature where DF is shown to be optimal. In less noisy relay channels, partial decode-and-forward (PDF) is shown to achieve the capacity. This is the third class of relay channels where PDF is shown to be optimal, where two previously known classes are the semideterministic relay channel and the relay channel with orthogonal components at the source. By using the definition of less noisy relay channel, we can easily construct many examples where DF is strictly suboptimal but PDF is capacity achieving.