Information Theory and Coding I - Exercises 12 14 Network Coding Butterfly Network The point-to-point transmission in networks has been dominated by routing and switching for a long time. In recent years the idea of network coding has tried to provide a gain for such a transmission. 1. Draw and explain a butterfly network as introduced in the lecture for wired networks and the case of one multicast transmission. Assuming binary single element packets, this means that one source produces two bits by and b2, which should be transmitted to two sinks t and t2. 2. Modify the butterfly network for the case of two unicast transmissions (two sources with one bit each, b + t2 and b2 + t). Show how much time can be saved via network coding compared to conventional routing/switching. 3. The butterfly network for wireless systems can be derived from the one for wired networks from 2 by merging the two inner nodes. Show that the gain of network coding can also be interpreted as an improvement of energy efficiency. Information Theory and Coding I - Exercises 12 14 Network Coding Butterfly Network The point-to-point transmission in networks has been dominated by routing and switching for a long time. In recent years the idea of network coding has tried to provide a gain for such a transmission. 1. Draw and explain a butterfly network as introduced in the lecture for wired networks and the case of one multicast transmission. Assuming binary single element packets, this means that one source produces two bits by and b2, which should be transmitted to two sinks t and t2. 2. Modify the butterfly network for the case of two unicast transmissions (two sources with one bit each, b + t2 and b2 + t). Show how much time can be saved via network coding compared to conventional routing/switching. 3. The butterfly network for wireless systems can be derived from the one for wired networks from 2 by merging the two inner nodes. Show that the gain of network coding can also be interpreted as an improvement of energy efficiency