Zero-error capacity

The zero-error capacity of a channel $p(y|x)$ is the maximum rate or reliable communication achievable under the requirement that the decoder produce the transmitted message almost surely. That is, the decoder can make no error. This is in contrast to the Shannon capacity, which allows the error to decay to zero asymptotically with the blocklength.

Connections to graph entropy
The zero-error capacity is related to the entropy of a graph associated to the channel.