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The primary aim of this paper is to present a new content-based, non-intrusive quality of experience (QoE) prediction model for low bitrate and resolution (QCIF) H.264 encoded videos and to illustrate its application in video quality adaptation over Universal Mobile Telecommunication Systems (UMTS) networks. The success of video applications over UMTS networks very much depends on meeting the QoE requirements of users. Thus, it is highly desirable to be able to predict and, if appropriate, to control video quality to meet such QoE requirements. Video quality is affected by distortions caused both by the encoder and the UMTS access network. The impact of these distortions is content dependent, but this feature is not widely used in non-intrusive video quality prediction models. In the new model, we chose four key parameters that can impact video quality and hence the QoE-content type, sender bitrate, block error rate and mean burst length. The video quality was predicted in terms of the mean opinion score (MOS). Subjective quality tests were carried out to develop and evaluate the model. The performance of the model was evaluated with unseen dataset with good prediction accuracy ( ~ 93%). The model also performed well with the LIVE database which was recently made available to the research community. We illustrate the application of the new model in a novel QoE-driven adaptation scheme at the pre-encoding stage in a UMTS network. Simulation results in NS2 demonstrate the effectiveness of the proposed adaptation scheme, especially at the UMTS access network which is a bottleneck. An advantage of the model is that it is light weight (and so it can be implemented for real-time monitoring), and it provides a measure of user-perceived quality, but without requiring time-consuming subjective tests. The model has potential applications in several other areas, including QoE control and optimization in network planning and content provisioning for network/service providers.