This paper studies the achievable rate for three-node discrete memoryless relay channel. Specifically in this mode, we explore two generalized feedbacks simultaneously： the source node actively collects feedback signals from the channel; and at the same time, the destination node actively transmits feedback signals to the relay node. These two feedback signals, which are called generalized feedback overheard from the channel that is likely to be noisy, induce that all the three nodes are in full duplex mode. The basic coding strategies of Cover and El Gamal are applied to the relay-source feedback transmission by the source forwarding the compressions of the channel output sequences at the relay node to the destination, and are also applied to the destination-relay feedback transmission to improve the decoding ability at the relay. Based on Cover and El Gamal coding, a new coding scheme adopting rate splitting and four-block Markov superposition encoding is proposed and the corresponding achievable rate is achieved. The proposed scheme is able to exploit two feedbacks simultaneously which can effectively eliminate underlying transmission bottlenecks for the channels. The derived achievable rate result generalizes several previously known results by including them as special cases.
