The Capacity of Several New Classes of Semi-Deterministic Relay Channels
The relay channel consists of a transmitter input x(1), a relay input x(2), a relay output y(2), and a receiver output y(3). In this paper, we establish the capacity of three new classes of semi-deterministic relay channels: 1) a class of degraded semi-deterministic relay channels, 2) a class of semi-deterministic orthogonal relay channels, and 3) a class of semi-deterministic relay channels with relay-transmitter feedback. For the first class of relay channels, the output of the relay y(2) depends on a deterministic function of the transmitter's input x(1), i.e., on s = f(1) (x(1)), rather than on x(1) directly. In addition, the relay channels satisfy the condition that S -> (X(2), Y(2)) -> Y(3) forms a Markov chain for all input probability distributions p (x(1), x(2)). Hence, the first class of relay channels includes, but is strictly not limited to, the class of degraded relay channels previously considered by Cover and El Gamal. The partial decode-and-forward strategy achieves the capacity of the class of degraded semi-deterministic relay channels. Next, we consider the class of semi-deterministic orthogonal relay channels where there are orthogonal channels from the relay to the receiver and from the transmitter to the receiver. In addition, the output of the relay y(2) is a deterministic function of x(1), x(2) and y(3), i.e., y(2) = f(4) (x(1), x(2), y(3)). The class of semi-deterministic orthogonal relay channels is a generalization of the class of deterministic relay channels considered by Kim. The compress-and-forward strategy achieves the capacity of the class of semi-deterministic orthogonal relay channels. For the third class of relay channels, there is a causal and noiseless feedback from the relay to the transmitter. In addition, similar to the second class of relay channels, the output of the relay y(2) is a deterministic function of x(1), x(2), and y(3). Both the generalized strategy of Gabbai and Bross and the hash-and-forward strategy of Kim achieve the capacity of the class of semi-deterministic relay channels with relay-transmitter feedback.
capacity semi-deterministic relay channel feedback decode-and-forward compress-and-forward hash-and-forward