We consider the estimation distortion of a distributed sensing system with finite number of sensor nodes, in which the nodes observe a common phenomenon and transmit their observations to a fusion center over orthogonal channels. In particular, we investigate whether the coded scheme (separate source-channel coding) outperforms the uncoded scheme (joint source-channel coding) or not. To this end, we explicitly derive the estimation distortion of a coded heterogeneous sensing system with diverse node and channel configurations. Based on this result, we show that in a homogeneous sensing system with identical node and channel configurations, the coded scheme outperforms the uncoded scheme if the number of nodes is $K=1$ or $K=2$. For homogenous sensing systems with $K\geq 3$ nodes and general heterogeneous sensing systems, we also present explicit conditions for the coded scheme to perform better than the uncoded scheme. Furthermore, we propose to minimize the estimation distortion of heterogeneous sensing systems with hybrid coding, i.e., some nodes use the coded scheme and other nodes use the uncoded scheme. To determine the optimal hybrid coding policy, we develop three greedy algorithms, in which the pure greedy algorithm minimizes distortion greedily, the group greedy algorithm improves performance by using a group of potential sub-polices, and the sorted greedy algorithm reduces computational complexity by using a pre-solved iteration order. Our numerical and Monte Carlo results show that the proposed algorithms closely approach the optimal policy in terms average estimation distortion.

中文翻译：

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具有正交多路访问的分布式传感：编码还是不编码？

我们考虑具有有限数量传感器节点的分布式传感系统的估计失真，其中节点观察共同现象并通过正交通道将它们的观察传输到融合中心。特别是，我们研究了编码方案（单独的源通道编码）是否优于未编码方案（联合源通道编码）。为此，我们明确地推导出具有不同节点和信道配置的编码异构传感系统的估计失真。基于此结果，我们表明，在具有相同节点和通道配置的同构传感系统中，如果节点数为$K=1$ 或者 $K=2$. 对于同质传感系统$K\geq 3$节点和一般异构传感系统，我们还提出了编码方案比未编码方案表现更好的明确条件。此外，我们建议使用混合编码来最小化异构传感系统的估计失真，即一些节点使用编码方案，而其他节点使用未编码方案。为了确定最优的混合编码策略，我们开发了三种贪心算法，其中纯贪心算法贪婪地最小化失真，群贪心算法通过使用一组潜在的子策略来提高性能，而排序贪心算法通过使用减少计算复杂度预先求解的迭代顺序。我们的数值和蒙特卡罗结果表明，所提出的算法在平均估计失真方面非常接近最优策略。