  The parity-oblivious random-access-code (PORAC) is a class of communication
games involving a sender (Alice) and a receiver (Bob). In such games, Alice's
amount of communication to Bob is constraint by the parity-oblivious (PO)
conditions, so that the parity information of her inputs remains oblivious to
Bob. The PO condition in an operational theory is equivalently represented in
an ontological model that satisfies the preparation noncontextuality. In this
paper, we provide a nontrivial generalization of the existing two-level PORAC
and derive the winning probability of the game in the preparation noncontextual
ontological model. We demonstrate that the quantum theory outperforms the
preparation noncontextual model by predicting higher winning probability in our
generalized PORAC.
