  In this paper, we consider the problem of distributed inference in tree based
networks. In the framework considered in this paper, distributed nodes make a
1-bit local decision regarding a phenomenon before sending it to the fusion
center (FC) via intermediate nodes. We propose the use of coding theory based
techniques to solve this distributed inference problem in such structures. Data
is progressively compressed as it moves towards the FC. The FC makes the global
inference after receiving data from intermediate nodes. Data fusion at nodes as
well as at the FC is implemented via error correcting codes. In this context,
we analyze the performance for a given code matrix and also design the optimal
code matrices at every level of the tree. We address the problems of
distributed classification and distributed estimation separately and develop
schemes to perform these tasks in tree networks. The proposed schemes are of
practical significance due to their simple structure. We study the asymptotic
inference performance of our schemes for two different classes of tree
networks: fixed height tree networks, and fixed degree tree networks. We show
that the proposed schemes are asymptotically optimal under certain conditions.
