Markov Chain Model for the Decoding Probability of Sparse Network Coding

Random linear network coding has been shown to offer an efficient communication scheme, leveraging a remarkable 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 sparse network coding (SNC), where only few packets are combined with each transmission. The amount of data packets to be combined can be set from a density parameter/distribution, which could be eventually adapted. In this paper, we present a semi-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 the means of a thorough simulation campaign, and the difference between model and simulation is negligible. We also include in the comparison of some 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 SNC techniques.