On information flow in relay networks

Preliminary investigations conducted by El Gamal and Cover (1980) have shown that a max-flow min-cut interpretation for the capacity expressions of the classes of degraded and semideterministic relay channels can be found. In this paper it is shown that such an interpretation can also be found for fairly general classes of discrete memoryless relay networks. Cover and El Gamal (1979) have obtained general lower and upper bounds to capacity. However, the capacity of the general relay channel is not known. Past results are here extended to establish the capacity of deterministic relay networks with no interference and degraded relay networks. A general upper bound is given to the capacity of any relay network with this upper bound being a natural generalization of Theorem 4 in the study conducted by Cover and El Gamal (1979).