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Motivated by recent emerging systems that can leverage partially correct packets in wireless networks, this paper proposes the novel concept of error estimating coding (EEC). Without correcting the errors in the packet, EEC enables the receiver of the packet to estimate the packet's bit error rate, which is perhaps the most important meta-information of a partially correct packet. Our EEC design provides provable estimation quality with rather low redundancy and computational overhead. To demonstrate the utility of EEC, we exploit and implement EEC in two wireless network applications, Wi-Fi rate adaptation and real-time video streaming. Our real-world experiments show that these applications can significantly benefit from EEC.