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Reliable and low latency multicast communication is important for futurevehicular communication. Sparse random linear network coding approach used toensure the reliability of multicast communication has been widely investigated.A fundamental problem of such communication is to characterize the decodingsuccess probability, which is given by the probability of a sparse randommatrix over a finite field being full rank. However, the exact expression forthe probability of a sparse random matrix being full rank is still unknown, andexisting approximations are recursive or not consistently tight. In this paper,we provide a tight and closed-form approximation to the probability of a sparserandom matrix being full rank, by presenting the explicit structure of thereduced row echelon form of a full rank matrix and using the product theorem.Simulation results show that our proposed approximation is of high accuracyregardless of the generation size, the number of coded packets, the field sizeand the sparsity, and tighter than the state-of-the-art approximations for alarge range of parameters.

The Decoding Success Probability of Sparse Random Linear Network Coding for Multicast