  In this paper, we study joint network coding and distributed source coding of
inter-node dependent messages, with the perspective of compressed sensing.
Specifically, the theoretical guarantees for robust $\ell_1$-min recovery of an
under-determined set of linear network coded sparse messages are investigated.
We discuss the guarantees for $\ell_1$-min decoding of quantized network coded
messages, using the proposed local network coding coefficients in \cite{naba},
based on Restricted Isometry Property (RIP) of the resulting measurement
matrix. Moreover, the relation between tail probability of $\ell_2$-norms and
satisfaction of RIP is derived and used to compare our designed measurement
matrix, with i.i.d. Gaussian measurement matrix. Finally, we present our
numerical evaluations, which shows that the proposed design of network coding
coefficients result in a measurement matrix with an RIP behavior, similar to
that of i.i.d. Gaussian matrix.
