Maximal decoding error probability (${\epsilon }_{\max }={\max }_w\mathrm{Pr}(d(Y)\ne w\mid W=w)$)

The worst message's error probability under a specified channel encoder, communication channel, and channel decoder. It upper-bounds the average error probability under every message probability distribution. In particular, a uniform bound on maximal decoding error probability remains valid after restricting to any nonempty subset of messages. This distinguishes it from an average-only error guarantee in channel coding.