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A new achievable rate based on a partial decoding scheme is proposed for the multilevel relay network. A novel application of regular encoding and backward decoding is presented to implement the proposed rate. In our scheme, the relays are arranged in feed-forward structure from the source to the destination. Each relay in the network decodes only part of the transmitted message by the previous relay. The proposed scheme differs from general parity forwarding scheme in which each relay selects some relays in the network but decodes all messages of the selected relays. It is also shown that in some cases higher rates can be achieved by the proposed scheme than previously known by Xie and  Kumar. For the classes of semideterministic and orthogonal relay networks, the proposed achievable rate is shown to be the exact capacity. The application of the defined networks is very well understood in wireless networking scenarios

A New Achievable Rate and the Capacity of Some Classes of Multilevel Relay Network