Approximate communication is being seriously considered as an effective technique for reducing power consumption and improving the communication efficiency of network-on-chips (NoCs). A major problem faced by these techniques is quality control: how do we ensure that the network will transmit data with sufficient accuracy for applications to produce acceptable results? Previous methods that addressed this issue require each application to calculate the approximation level for every piece of approximable data, which takes hundreds of cycles. So the approximation information is often not available when a request packet is transmitted. Therefore, the reply packet with the approximable data is transmitted with unnecessarily absolute accuracy, reducing the effectiveness of approximate communication. In this paper, we propose a hardware-based quality management framework for approximate communication to minimize the time needed for the approximation level calculation. The proposed framework employs a configuration algorithm to continuously adjust the quality of every piece of data based on the difference between the output quality and the application's quality requirement. When the proposed framework is implemented in a network, every request packet can be transmitted with the updated approximation level. This framework results in fewer flits in each data packet and reduces traffic in NoCs while meeting the quality requirements of applications. Our cycle-accurate simulation using the AxBench benchmark suite shows that the proposed online quality management framework can reduce network latency by up to 52% and dynamic power consumption by 59% compared to previous approximate communication techniques while ensuring 95% output quality. This hardware-software codesign incurs 1% area overhead over previous techniques.