The importance of tie-breaking in finite-blocklength bounds

Upper bounds on the error probability in channel coding are considered, improving the RCU bound by taking into account events, where the likelihood of the correct codeword is tied with that of some competitors. This bound is compared to various previous results, both qualitatively and quantitatively; it is shown to be the tightest bound with respect to previous bounds with the same computational complexity. With respect to maximal error probability of linear codes, it is observed that when the channel is additive, the derivation of bounds, as well as the assumptions on the admissible encoder and decoder, simplify considerably.