  We consider a network coding setting where some of the messages and edges
have fixed alphabet sizes, that do not change when we increase the common
alphabet size of the rest of the messages and edges. We prove that the problem
of deciding whether such network admits a coding scheme is undecidable. This
can be considered as a partial solution to the conjecture that network coding
(without fixed-size messages/edges) is undecidable. The proof, which makes
heavy use of analogies with digital circuits, is essentially constructing a
digital circuit of logic gates and flip-flops within a network coding model
that is capable of simulating an arbitrary Turing machine.
