Sparse random linear network coding for data compression in WSNs

This paper addresses the information theoretical analysis of data compression achieved by random linear network coding in wireless sensor networks. A sparse network coding matrix is considered with columns having possibly different sparsity factors. For stationary and ergodic sources, necessary and sufficient conditions are provided on the number of required measurements to achieve asymptotically vanishing reconstruction error. To ensure the asymptotically optimal compression ratio, the sparsity factor can be arbitrary close to zero in absence of additive noise. In presence of noise, a sufficient condition on the sparsity of the coding matrix is also proposed.