In wireless networks, designing transmission schemes that can adapt to time-varying channel conditions is key to improving spectral efficiency. However, the realization of such schemes for multihop wireless networks is challenging, owing to the requirement of coordination among nodes. As coordination through the use of feedback between nodes incurs significant bandwidth penalty, spectral efficiency can be improved by minimizing traffic in the feedback channel. This paper proposes an adaptive rate transmission scheme using incremental-redundancy-based cooperative coding that minimizes the required feedback. By exploiting the inherent implicit feedback channel during relaying, the spectral efficiency of multihop wireless networks can be improved considerably. Rather than allocating dedicated channels to feedback the quality of information at the relay, the implicit feedback channel measures such information and determines the transmitter for the additional coded (redundancy) bits. This optimizes the throughput. The proposed scheme is thoroughly analyzed under different deployment environments. Theoretical bounds for the proposed scheme are presented and supported with results from extensive simulation studies.