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In practice, since many communication networks are huge in scale orcomplicated in structure even dynamic, the predesigned network codes based onthe network topology is impossible even if the topological structure is known.Therefore, random linear network coding was proposed as an acceptable codingtechnique. In this paper, we further study the performance of random linearnetwork coding by analyzing the failure probabilities at sink node fordifferent knowledge of network topology and get some tight and asymptoticallytight upper bounds of the failure probabilities. In particular, the worst casesare indicated for these bounds. Furthermore, if the more information about thenetwork topology is utilized, the better upper bounds are obtained. Thesebounds improve on the known ones. Finally, we also discuss the lower bound ofthis failure probability and show that it is also asymptotically tight.

The Failure Probability at Sink Node of Random Linear Network Coding