Upper bounds for the failure probability of random linear network coding for multicast network

The random linear network coding was proposed as an adoptable coding technique for many practical communication networks. This study focuses on analysing the failure probabilities of random linear network coding to study its performance for multicast network, emphatically some known upper bounds of the failure probabilities have been improved and the worst cases are indicated for these bounds. Besides, if the more network topology information is achieved, the better upper bounds can be obtained. Furthermore when the field size goes to infinity the limit behaviours of the failure probabilities are discussed.