We investigate covert channels that use players moves to transmit information. We assume that there exits noise generated by periods of invisiblility of the transmitting player (due to network failures, game mechanics, etc.); thus there arises the problem of reliable transmission of information over a noisy channel. The formal model that addresses this problem is referred to as a structure of partial erasure. In the framework of the model we prove the criterion of equivalence of a pair of trajectories on the receiving end of the channel. We also discuss a number of methods that prevent organization of covert channels of the type considered.