  In this paper, we study the data gathering problem in the context of power
grids by using a network of sensors, where the sensed data have inter-node
redundancy. Specifically, we propose a new transmission method, calledquantized
network coding, which performs linear net-work coding in the field of real
numbers, and quantization to accommodate the finite capacity of edges. By using
the concepts in compressed sensing literature, we propose to use
l1-minimization to decode the quantized network coded packets, especially when
the number of received packets at the decoder is less than the size of sensed
data (i.e. number of nodes). We also propose an appropriate design for network
coding coefficients, based on restricted isometry property, which results in
robust l1-min decoding. Our numerical analysis show that the proposed quantized
network coding scheme with l1-min decoding can achieve significant
improvements, in terms of compression ratio and delivery delay, compared to
conventional packet forwarding.
