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The quality-of-service (QoS) guarantees enabled by the new IEEE 802.11 a/e Wireless LAN (WLAN) standard are specifically targeting the real-time transmission of multimedia content over the wireless medium. Since video data consume the largest part of the available bitrate compared to other media, optimization of video streaming for this new standard is a significant factor for the successful deployment of practical systems. Delay-constrained streaming of fully-scalable video over IEEE 802.11 a/e WLANs is of great interest for many multimedia applications. The new medium access control (MAC) protocol of IEEE 802.11e is called the Hybrid Coordination Function (HCF) and, in this paper, we will specifically consider the problem of video transmission over HCF Controlled Channel Access (HCCA). A cross-layer optimization across the MAC and application layers of the OSI stack is used in order to exploit the features provided by the combination of the new HCCA standard with new versatile scalable video coding algorithms. Specifically, we propose an optimized and scalable HCCA-based admission control for delay-constrained video streaming applications that leads to a larger number of stations being simultaneously admitted (without quality reduction to any video flow). Subsequently, given the allocated transmission opportunity, each station deploys an optimized Application-MAC-PHY adaptation, scheduling, and protection strategy that is facilitated by the fine-grain layering provided by the scalable bitstream. Given that each video flow needs to always comply with the predetermined (a priori negotiated) traffic specification parameters, this cross-layer strategy enables graceful quality degradation whenever the channel conditions or the video sequence characteristics change. For instance, it is demonstrated that the proposed cross-layer protection and bitstream adaptation strategies facilitate QoS token rate adaptation under link adaptation mechanisms that utilize different physical layer transmission rates. The expected gains offered by the optimized solutions proposed in this paper are established theoretically, as well as through simulations.