To enhance video streaming experience for mobile users, we propose an approach towards Quality-of-Experience (QoE) aware on-the-fly transcoding. The proposed approach relies on the concept of Mobile Edge Computing (MEC) as a key enabler in enhancing service quality. Our scheme involves an autonomic creation of a transcoding service as a Virtual Network Function (VNF) and ensures dynamic rate switching of the streamed video to maintain the desirable quality. This edge-assistive transcoding and adaptive streaming results in reduced computational loads and reduced core network traffic. The proposed solution represents a complete miniature content delivery network infrastructure on the edge, ensuring reduced latency and better quality of experience