  We consider a joint sampling and compression system for timely status
updates.
  Samples are taken, quantized and encoded into binary sequences, which are
sent to the destination.
  We formulate an optimization problem to jointly design sampler, quantizer and
encoder, minimizing the age of information (AoI) on the basis of satisfying a
mean-squared error (MSE) distortion constraint of the samples.
  We prove that the zero-wait sampling, the uniform quantization, and the
real-valued AoI-optimal coding policies together provide an asymptotically
optimal solution to this problem, i.e., as the average distortion approaches
zero, the combination achieves the minimum AoI asymptotically.
  Furthermore, we prove that the AoI of this solution is asymptotically linear
with respect to the log MSE distortion with a slope of $-\frac{3}{4}$.
  We also show that the real-valued Shannon coding policy suffices to achieve
the optimal performance asymptotically.
  Numerical simulations corroborate the analysis.
