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The Extended RItz Method (ERIM) can be used to face optimal decision and control problems when finding the global solution is hard, because the problem is ill-conditioned or we can only compute the solution via numerical approximations. It consists in constraining the control functions to take on a fixed structure with a certain number of free parameters to be optimized. We will show the use of such method for the solution of a communication problem in a mixed (analog/digital) transmission environment. A noisy channel is used to convey information from a limited-energy analog device to a sink; in the presence of a binary link, how can we reduce the energy spent for transmission without renouncing reconstruction capability and real-time encoding?