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