Reliable computation of nomographic functions over Gaussian multiple-access channels

In this paper, a wireless sensor network is considered in which the objective is not to communicate individual sensor readings over a Gaussian multiple-access channel to a fusion center but rather to reliably compute some nomographic function thereof. Nomographic functions are exactly those multivariate functions that can be represented as a post-processed sum of pre-processed sensor readings. This special structure permits the utilization of the interference property of the Gaussian multiple-access channel for computing some nomographic functions at significantly higher rates than those achievable with traditional schemes. In this paper, a corresponding coding scheme is presented that protects the sum of pre-processed sensor readings against the channel noise by letting each node use the same nested lattice code.