标题： 马尔可夫链的最优信源编码用于实时远程估计 显示英文标题

标题： Optimal Source Coding of Markov Chains for Real-Time Remote Estimation

摘要： 我们重新考虑在传输时间和马尔可夫链状态转换发生在同一时间尺度下的马尔可夫链的信源编码问题。 具体来说，我们假设每个比特的传输占用一个时间槽，马尔可夫链在同一时间槽内更新其状态。 因此，分配给一个符号的码字长度决定了未传输符号的数量，以及下一个要传输符号实现的概率。 我们的目标是通过提出一种基于最后一次传输符号及其传输持续时间的最优信源编码策略，来最小化无限时间范围内的平均传输持续时间。 为了找到最优策略，我们通过将符号与符号的传输持续时间相结合，以马尔可夫决策过程（MDP）的形式来构建该问题。 最后，我们分析了两种基于霍夫曼的基准策略，并将其性能与所提出的最优策略进行比较。 我们观察到，在随机生成的过程中，所提出的最优策略相比基准策略减少了平均传输持续时间。 性能提升根据马尔可夫过程的参数而有所不同。 显示英文摘要

摘要： We revisit the source coding problem for a Markov chain under the assumption that the transmission times and how fast the Markov chain transitions its state happen at the same time-scale. Specifically, we assume that the transmission of each bit takes a single time slot, and the Markov chain updates its state in the same time slot. Thus, the length of the codeword assigned to a symbol determines the number of non-transmitted symbols, as well as, the probability of the realization of the next symbol to be transmitted. We aim to minimize the average transmission duration over an infinite horizon by proposing an optimal source coding policy based on the last transmitted symbol and its transmission duration. To find the optimal policy, we formulate the problem with a Markov decision process (MDP) by augmenting the symbols alongside the transmission duration of the symbols. Finally, we analyze two Huffman-based benchmark policies and compare their performances with the proposed optimal policy. We observe that, in randomly generated processes, our proposed optimal policy decreases the average transmission duration compared to benchmark policies. The performance gain varies based on the parameters of the Markov process.