The problem of finding the optimal node density for reconstructing a stochastic signal from its noisy samples in sensor networks is considered. The signal could be nonstationary and nonbandlimited. A weight is assigned to each location that indicates the relative importance of the signal at that location. It is shown that when the number of samples is very large, the optimal density of the samples at each location is proportional to the square root of the weight associated to that location.

We study the problem of transmission of binary input non-linear functions over a network of mobiles based on CDMA. Motivation for this study comes from the application of using cheap measurement devices installed on personal cellphones to monitor environmental parameters such as air pollution, temperature and noise level. Our model resembles the MAC model of Nazer and Gastpar except that the encoders are restricted to be CDMA encoders. Unlike the work of Nazer and Gastpar whose main attention is transmission of linear functions, we deal with non-linear functions with binary inputs. A main contribution of this paper is a lower bound on the computational capacity for this problem. While in the traditional CDMA system the signature matrix of the CDMA system preferably has independent rows, here the signature matrix of the CDMA system is viewed as the parity check matrix of a linear code, reflecting our treatment of the interference. We also introduce the problem of Slepian-Wolf compression with the same compression matrix.