On group network codes: Ingleton-bound violations and independent sources

In principle, network codes derived from non-Abelian groups can be used to attain every point in the capacity region of wired acyclic networks. However, group codes derived from a particular group, and its subgroups, is useful only if it can model independent sources, as well as violate the Ingleton bound which restricts the capacity region obtainable by linear network codes. We study both the independent source and the Ingleton-violating requirement for subgroups of the groups PGL(2, ρ) and GL(2, ρ) with primes ρ ≥ 5. For both these groups we demonstrate that the requirements can be met, which suggests that PGL(2, ρ) and GL(2, ρ) are rich enough groups to construct network codes superior to linear ones. We also construct a model for independent sources using the direct product of the aforementioned groups.