On the Problem of Adding Infinitely Many Values

Average consensus is a decentralized computation algorithm for calculating the average of the state variables of the nodes in a network. Over wireless networks, it is typically implemented using point-to-point random access scheduling. Wireless communications, however, are interference limited and when the available bandwidth is fixed, the expected delay in achieving a certain precision in the average value increases as the network size scales up. We show that this limitation in large networks disappears if we use specially structured codes. We analyze a combined source and channel coding strategy that uses an incoherent combination of power over orthogonal subchannels for the average consensus protocol. We show that in spite of the bandwidth and power limitations, with our simple strategy the delay and precision can be kept bounded while increasing the number of participants.