  Encoding and decoding are the two key steps in information processing. In
this work we study the encoding and decoding capabilities of operational
theories in the context of information-storability game, where the task is to
freely choose a set of states from which one state is chosen at random and by
measuring the state it must be identified; a correct guess results in as many
utiles as the number of states in the chosen set and an incorrect guess means a
penalty of a fixed number of utiles. We connect the optimal winning strategy of
the game to the amount of information that can be stored in a given theory,
called the information storability of the theory, and show that one must use
so-called nondegradable sets of states and nondegradable measurements whose
encoding and decoding properties cannot be reduced. We demonstrate that there
are theories where the perfect discrimination strategy is not the optimal one
so that the introduced game can be used as an operational test for super
information storability. We further develop the concept of information
storability by giving new useful conditions for calculating it in specific
theories.
