We consider the problem of broadcasting in the presence of linearly bounded number of transient faults. For some fixed 0 <α < 1 we assume that at most αi faulty transmissions can occur during the first i time units of the broadcasting algorithm execution, for every natural i. In a unit of time every node can communicate with at most one neighbor. We prove that some bounded degree networks are robust with respect to linearly bounded transmission faults for any 0 < α < 1, and give examples of such networks with logarithmic broadcast time, thus solving the open problem from Ga̧sieniec and Pelc (1998). We also show that our broadcasting algorithm is asymptotically optimal in terms of message complexity.
