Criterion for the existence of a consistent protocol in a partial erasure channel

Covert channels allow one to transmit information using mechanisms that were not originally intended for transmission. An example is a process in which a transmitter encodes information in moves of a character of a multiplayer game, and a receiver observes the moves and decodes the original message. This channel may be noisy, since the character may fall out of the receiver's sight, a number of network packets may be lost, etc. Thus there emerges a natural problem of ogranizing a reliable channel. We propose a formal model called a partial erasure channel that describes the interaction of a transmitter and a receiver, introduce the notion of a consistent transmission protocol, formulate and prove the consistency criterion on the transmitting side and construct the optimal receiver for the given consistent transmitter.