Network coding encourages in-network mixing of information flows for enhanced network capacity, particularly for multicast data dissemination. While existing theory on multicast network coding often treats the underlying network topology as a blackbox, we explore network-specific properties in the topology to design efficient code assignment algorithms over small field sizes.
This thesis studies planar and pseudo planar networks, under the basic yet fundamental setting of multicasting two information flows to an arbitrary number of receivers. We show that routing is equivalent to coding in outerplanar networks; GF(2) suffices in a planar network if all relay nodes reside on the same face; for general planar networks, coding over GF(3) is sufficient; and for apex networks which are almost planar except for one node, coding over GF(4) suffices. A linear time code assignment algorithm is further extracted from the constructive proof in each case.