Quantized network coding for sparse messages

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, called quantized network coding, which performs linear network coding in the infinite 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.