Semantic source coding for two users with heterogeneous goals

We study a multiuser system in which an information source provides status updates to two monitors with heterogeneous goals. Semantic filtering is first performed to select the most useful realizations for each monitor. Packets are then encoded and sent so that each monitor can timely fulfill its goal. In this regard, some realizations are important for both monitors, while every other realization is informative for only one monitor. We determine the optimal real codeword lengths assigned to the selected packet arrivals in the sense of maximizing a weighted sum of semanticsaware utility functions for the monitors. Our analytical and numerical results provide the optimal design parameters for different arrival rates and highlight the improvement in timely status update delivery using semantic filtering and source coding.