  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 $K\geq3$ 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.
