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This paper proposes a relay-assisted re-transmission scheme based on mutual information for wireless mesh networks. In the proposed scheme, re-transmission is done not from the source node but from the relay node, and minimal amount of spectrum corresponding to the remaining uncertainty for the data sequence is re-transmitted, where the number of spectrum components to be fed back is determined based on expected mutual information after re-transmission. Moreover, to directly convert reduction of feedback spectrum to spectrum efficiency improvement in carrier sense multiple access with collision avoidance (CSMA/CA) introduced systems, the re-transmitted spectrum is mapped on whole the bandwidth with equal spacing, thereby the time duration for the re-transmission is reduced. Computer simulation confirms that the proposed scheme can achieve much higher system throughput efficiency especially than the conventional two-hop transmission schemes.