For the multiple-level relay channel, an achievable rate formula, and a simple coding scheme to achieve it, are presented. Generally, higher rates can be achieved with this coding scheme in the multiple-level relay case than previously known. For a class of degraded channels, this achievable rate is shown to be the exact capacity. An application of the coding scheme to the allcast problem is also discussed. Index Terms-Channel with feedback, degraded channel, multiple-relay channel, multiuser information theory, network information theory. I. INTRODUCTION T HE relay channel was introduced by van der Meulen [1], [2]. The simplest case, shown in Fig. 1, is the three-node scenario where node 1 functions purely as a relay to help the information transmission from node 0 to node 2. An immediate application of this framework, for instance, is in wireless communications, where a node is placed between the source node and the destination node, in order to shorten the distance of a hop, which has implications in terms of the amount of traffic carried, interference, power consumption, etc. In [1], a special discrete memoryless relay channel is even constructed for which no reliable information transmission is possible without the help of the relay node. The simplest discrete memoryless one-relay channel is depicted in Fig. 1, where nodes 0, 1, and 2 are the source, the relay, and the destination, respectively. This channel can be denoted by , where , are the transmitter alphabets of nodes 0 and 1, respectively, and are the receiver alphabets of nodes 1 and 2, respectively, and a collection of probability distributions on , one for each. The interpretation is that is the input to the channel from the source node 0, is the output Manuscript