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This thesis investigates the problem of robust coding and error concealment in High Efficiency Video Coding (HEVC). After a review of the current state of the art, a simulation study about error robustness, revealed that the HEVC has weak protection against network losses with significant impact on video quality degradation. Based on this evidence, the first contribution of this work is a new method to reduce the temporal dependencies between motion vectors, by improving the decoded video quality without compromising the compression efficiency. The second contribution of this thesis is a two-stage approach for reducing the mismatch of temporal predictions in case of video streams received with errors or lost data. At the encoding stage, the reference pictures are dynamically distributed based on a constrained Lagrangian rate-distortion optimization to reduce the number of predictions from a single reference. At the streaming stage, a prioritization algorithm, based on spatial dependencies, selects a reduced set of motion vectors to be transmitted, as side information, to reduce mismatched motion predictions at the decoder. The problem of error concealment-aware video coding is also investigated to enhance the overall error robustness. A new approach based on scalable coding and optimally error concealment selection is proposed, where the optimal error concealment modes are found by simulating transmission losses, followed by a saliency-weighted optimisation. Moreover, recovery residual information is encoded using a rate-controlled enhancement layer. Both are transmitted to the decoder to be used in case of data loss. Finally, an adaptive error resilience scheme is proposed to dynamically predict the video stream that achieves the highest decoded quality for a particular loss case. A neural network selects among the various video streams, encoded with different levels of compression efficiency and error protection, based on information from the video signal, the coded stream and the transmission network. Overall, the new robust video coding methods investigated in this thesis yield consistent quality gains in comparison with other existing methods and also the ones implemented in the HEVC reference software. Furthermore, the trade-off between coding efficiency and error robustness is also better in the proposed methods.