  We show that iterative coding systems can not surpass capacity using only
quantities which naturally appear in density evolution. Although the result in
itself is trivial, the method which we apply shows that in order to achieve
capacity the various components in an iterative coding system have to be
perfectly matched. This generalizes the perfect matching condition which was
previously known for the case of transmission over the binary erasure channel
to the general class of binary-input memoryless output-symmetric channels.
Potential applications of this perfect matching condition are the construction
of capacity-achieving degree distributions and the determination of the number
required iterations as a function of the multiplicative gap to capacity.
