  The effects of quantization and coding on the estimation quality of a
Gauss-Markov, namely Ornstein-Uhlenbeck, process are considered. Samples are
acquired from the process, quantized, and then encoded for transmission using
either infinite incremental redundancy or fixed redundancy coding schemes. A
fixed processing time is consumed at the receiver for decoding and sending
feedback to the transmitter. Decoded messages are used to construct a minimum
mean square error (MMSE) estimate of the process as a function of time. This is
shown to be an increasing functional of the age-of-information, defined as the
time elapsed since the sampling time pertaining to the latest successfully
decoded message. Such (age-penalty) functional depends on the quantization
bits, codeword lengths and receiver processing time. The goal, for each coding
scheme, is to optimize sampling times such that the long term average MMSE is
minimized. This is then characterized in the setting of general increasing
age-penalty functionals, not necessarily corresponding to MMSE, which may be of
independent interest in other contexts.
