The rate transfer argument in two-stage scenarios: When does it matter?

The significance of the rate transfer argument used in a class of two-stage source and channel coding problems is discussed. A very simple necessary and sufficient condition is derived as to when the argument helps expand the achievability region. Special attention is paid to several example scenarios such as successive refinement with or without side information, and degraded broadcast channels. Finally, for reliable separate source-channel coding, whether a test based on comparing marginal source and channel rate regions is more restrictive than comparing cumulative rate regions, obtained after using the rate transfer argument, is discussed. It turns out that if rate transfer does not matter in either the source or the channel coding problem, the two tests are equivalent.