Decentralized Inference Over Multiple-Access Channels

The problem of decentralized inference over multiple-access fading channels is considered from a joint source-channel coding perspective. In our setting, spatially distributed wireless sensor nodes collect observation data about a hidden source and communicate relevant statistics to a receiver node that generates the desired inference (estimation or detection) about unknown source parameters. We assume a homogeneous sensor signal field in which information about the source parameters is distributed in space (across sensors) and time in an independent and identically distributed (i.i.d.) manner. Our study characterizes the asymptotic performance of an identical source-channel mapping for i.i.d. sensor observation data in which the same encoder is used at all the nodes. This scheme generalizes many existing methods including uncoded transmission and type-based multiple access. Sufficient conditions are obtained under which our identical mapping approach achieves the genie-aided scaling law (in the number of nodes) associated with a noiseless channel, even when the nodes transmit with asymptotically vanishing power. Our analysis also elucidates the critical impact of channel state information on the achievable performance. In particular, it identifies scenarios in which identical mapping fails and a simple nonidentical mapping scheme is shown to improve performance. Numerical examples are provided to illustrate the theoretical principles derived in the paper.