We study a system in which two-state Markov sources send status updates to a common receiver over a slotted ALOHA random access channel. We characterize the performance of the system in terms of state estimation entropy (SEE), which measures the uncertainty at the receiver about the sources' state. Two channel access strategies are considered, a reactive policy that depends on the source behavior and a random one that is independent of it. We prove that the considered policies can be studied using two different hidden Markov models (HMM) and show through density evolution (DE) analysis that the reactive strategy outperforms the random one in terms of SEE while the opposite is true for AoI. Furthermore, we characterize the probability of error in the state estimation at the receiver, considering a maximum a posteriori (MAP) estimator and a low-complexity (decode and hold) estimator. Our study provides useful insights on the design trade-offs that emerge when different performance metrics such as SEE, age or information (AoI) or state estimation error probability are adopted. Moreover, we show how the source statistics significantly impact the system performance.

翻译：我们研究了一个系统，其中两状态马尔可夫源通过时隙ALOHA随机接入信道向公共接收器发送状态更新。我们利用状态估计熵（SEE）来刻画系统性能，该指标衡量接收器对源状态的不确定性。考虑了两种信道接入策略：一种依赖于源行为的反应式策略，另一种与之无关的随机策略。我们证明所考虑的策略可通过两种不同的隐马尔可夫模型（HMM）进行研究，并通过密度演化（DE）分析表明，反应式策略在SEE方面优于随机策略，而年龄信息（AoI）方面的结论则相反。此外，我们基于最大后验（MAP）估计器和低复杂度（解码并保持）估计器，刻画了接收器处状态估计的误差概率。本研究为采用不同性能指标（如SEE、年龄信息（AoI）或状态估计误差概率）时产生的设计权衡提供了有用见解。此外，我们展示了源统计特征对系统性能的显著影响。