On the performance of joint and separate channel and network coding in wireless fading networks

For wireless fading networks where M source nodes wish to multicast their information to N destination nodes via a common relay, it has been shown that network coding at the relay can reduce the number of required transmissions, if the destination nodes overhear M - 1 source nodes transmitting to the relay. Nested coding is a recently proposed alternative where, unlike network coding, physical and network layers are jointly designed. We find that for a given network throughput ideal nested coding in many situations can lead to a significant increase in transmission reliability compared to network coding. We also consider the case of feedback and retransmissions when received packets fail to be decoded. For the case of two source nodes it is shown that by using nested codes the expected number of relay transmissions is reduced. However, for a larger number of source nodes the gain depends on the employed nested coding strategy at the relay.