We study the problem of universal decoding over memoryless channels with a decoder based on the Krichevsky-Trofimov estimator. We show that this decoder is random-coding universal for codebooks of any size, i.e., despite being ignorant of the channel in use, it has asymptotically the same random-coding error exponent as the optimal maximum-likelihood decoder for that channel. Then, we incorporate this decoding rule in schemes to decode practical linear block codes and convolutional codes when the channel is unknown to the receiver. Numerical results show that efficient performance can be achieved even for moderate blocklength or constraint length.