  We show that optimal protocols for noisy channel coding of public or private
information over either classical or quantum channels can be directly
constructed from two more primitive information-theoretic tools: privacy
amplification and information reconciliation, also known as data compression
with side information. We do this in the one-shot scenario of structureless
resources, and formulate our results in terms of the smooth min- and
max-entropy. In the context of classical information theory, this shows that
essentially all two-terminal protocols can be reduced to these two primitives,
which are in turn governed by the smooth min- and max-entropies, respectively.
In the context of quantum information theory, the recently-established duality
of these two protocols means essentially all two-terminal protocols can be
constructed using just a single primitive.
