Real-Time Status Updates for Markov Source

For timely sensor update, the traditional approach is to send new information at every available opportunity. Recent research has shown that with limited receiver feedback, sensors can improve the update timeliness by transmitting differential information for slowly varying correlated sources. One can elect to transmit either the actual or the differential state information based on a differential encoding threshold for a general Markov source. This threshold captures the natural trade-off between differential transmission opportunities and the coding gains. Using matrix-geometric method, we find the limiting age distribution for a Markov source as a function of the encoding threshold, from which several other performance metrics of interest, such as mean age, peak age, and the probability of decoding failure can be derived.