Random linear network coding with source precoding for multi-session networks

While random linear network coding (RLNC) asymptotically achieves the capacity of single-session multicast networks, it is sub-optimal in general for multi-session networks, since with RLNC, the inter-session interference is mixed with the desired information to the largest extend. In general, finding the optimal network code for multi-session networks is challenging. In this chapter, we show that effective network codes can be constructed for some classes of multi-session networks by applying RLNC at the intermediate nodes, together with properly designed linear precoding at the source nodes that minimize the inter-session interference. Specifically, we design the optimal precoding scheme and derive the achievable rate region for double-unicast networks with RLNC applied at the intermediate nodes. We also show that the capacity of multi-source single-sink erasure networks can be asymptotically achieved by RLNC with random linear precoder over a sufficiently large number of time extensions.