We survey recent and not-so-recent upper bounds on the error probability in
channel coding. We shed light on the relation between bounds derived using
maximum-likelihood and threshold decoding, and specifically on the role of
tie-breaking. With respect to maximal error probability of linear codes, we
observe that when the channel is modulo-additive, the derivation of bounds, as
well as the assumptions on the admissible encoder and decoder, simplify
considerably.