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In order to exploit the full degrees of freedom of multi-antenna multi-user systems, accurate channel state information at the transmitter is needed. We consider a low latency and low complexity design for a closed-loop channel state information feedback scheme, where user terminals feed back their channel state information simultaneously to a multi-antenna base station. The underlying theoretical problem consists of the lossy transmission of multiple independent analog sources over a Gaussian MIMO Multi-Access Channel (MIMO-MAC), under a Mean-Square Error (MSE) criterion. We analyze distortion exponent, i.e., the order of decrease of the channel state information MSE for increasing channel SNR, and design very simple "almost uncoded" schemes that outperform conventional approaches such as finite-rate feedback and uncoded "analog" feedback.