We consider a source monitoring a stochastic process with a transmitter to transmit timely information through a wireless ON/OFF channel to a destination. We assume that once the source samples the data, the sampled data has to be processed to identify the state of the stochastic process. The processing can take place either at the source before transmission or after transmission at the destination. The objective is to minimize the distortion while keeping the age of information (AoI) that measures the timeliness of information under a certain threshold. We use a stationary randomized policy (SRP) framework to solve the formulated problem. We show that the two-dimensional discrete-time Markov chain considering the AoI and instantaneous distortion as the state is lumpable and we obtain the expression for the expected AoI under the SRP.

翻译：我们考虑一个信源监测随机过程，通过无线ON/OFF信道向目的地传输及时信息。假设信源采样数据后，需对采样数据进行处理以识别随机过程的状态。该处理既可在传输前于信源处完成，也可在传输后于目的地进行。目标是在将衡量信息时效性的信息年龄（AoI）保持在特定阈值以下的同时，最小化失真。我们采用平稳随机策略（SRP）框架求解该问题。研究表明，以AoI与瞬时失真为状态的二维离散时间马尔可夫链具有可折叠性，并推导出SRP下期望AoI的表达式。