  The Kraft inequality gives a necessary and sufficient condition for the
existence of a single channel prefix-free code. However, the multichannel Kraft
inequality does not imply the existence of a multichannel prefix-free code in
general. It is natural to ask whatever there exists an efficient decision
procedure for the existence of multichannel prefix-free codes. In this paper,
we tackle the two-channel case of the above problem by relating it to a
constrained rectangle packing problem. Although a general rectangle packing
problem is NP-complete, the extra imposed constraints allow us to propose an
algorithm which can solve the problem efficiently.
