Towards Efficient Designs for In-network Computing with Noisy Wireless Channels

In this paper we study distributed function computation in a noisy multi-hop wireless network, in which $n$ nodes are uniformly and independently distributed in a unit square. We adopt the adversarial noise model, for which independent binary symmetric channels are assumed for any point-to-point transmissions, with (not necessarily identical) crossover probabilities bounded above by some constant ε. Each node holds an m-bit integer per instance and the computation is started after each node collects N readings. The goal is to compute a global function with a certain fault tolerance, in this distributed setting; we mainly deal with divisible functions, which essentially covers the main body of interest for wireless applications. We focus on protocol designs that are efficient in terms of communication complexity. We first devise a general protocol for evaluating any divisible functions, addressing both one-shot (N = O(1)) and block computation, and both constant and large $m$ scenarios; its bottleneck in different scenarios is also analyzed. Based on this analysis, we then endeavor to improve the design for two special cases: identity function, and some restricted type-threshold functions, both focusing on the constant m and N scenario.