Given a system modeled by a rational relation R, a channel is a pair (E,D) of rational relations that respectively encode and decode binary messages, and such that the composition E R D is the identity relation. This means that the message between E and D has been perfectly transmitted through R. Investigating the links between channels and the growth of rational sets of words, we give new characterizations for relations with channels. In the particular case where the relation is given as a union of functions, we obtain as a consequence the decidability of the synthesis problem with a linear complexity.