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In live video communication, the quality of the video that is encoded on a mobile device is more often than not constrained by the available computational resources. We address this problem by allowing the encoder to “outsource” the encoding complexity to the decoder through the use of feedback, under a sum-rate constraint comprising the weighted sum of the forward and feedback rates. Analysis of such a complexity-outsourced framework using an analytically tractable video model reveals that the feedback rate should be optimally adapted to the video motion characteristics. Application of our framework to real-world video sequences reveals the efficacy of our proposed architecture, with experimental results validating that substantial gains in PSNR are achievable over state-of-the-art fast-search algorithms at a comparable level of complexity. These gains are significant even for mobile live video communication applications over the Internet.