  Random Linear Network Coding (RLNC) has been proved to offer an efficient
communication scheme, leveraging an interesting robustness against packet
losses. However, it suffers from a high computational complexity and some novel
approaches, which follow the same idea, have been recently proposed. One of
such solutions is Tunable Sparse Network Coding (TSNC), where only few packets
are combined in each transmissions. The amount of data packets to be combined
in each transmissions can be set from a density parameter/distribution, which
could be eventually adapted. In this work we present an analytical model that
captures the performance of SNC on an accurate way. We exploit an absorbing
Markov process where the states are defined by the number of useful packets
received by the decoder, i.e the decoding matrix rank, and the number of
non-zero columns at such matrix. The model is validated by means of a thorough
simulation campaign, and the difference between model and simulation is
negligible. A mean square error less than $4 \cdot 10^{-4}$ in the worst cases.
We also include in the comparison some of more general bounds that have been
recently used, showing that their accuracy is rather poor. The proposed model
would enable a more precise assessment of the behavior of sparse network coding
techniques. The last results show that the proposed analytical model can be
exploited by the TSNC techniques in order to select by the encoder the best
density as the transmission evolves.
