log10Perror

log10Perror is a notation used in statistics, coding theory, and signal processing to denote the base-10 logarithm of the probability of error (P_error) associated with a detector, classifier, or communication system.

P_error is the probability that the decision is incorrect; log10Perror = log10(P_error). Since 0 ≤ P_error ≤ 1, log10Perror ≤ 0, with more negative values indicating lower error probabilities.

Applications and contexts: used when error probabilities vary over several orders of magnitude; common in evaluating receivers, classifiers, and error-correcting codes; provides a compact scale for plotting and comparison.

Calculation: depends on the model; can be computed directly from known P_error, or via a closed-form expression for specific channels (for example, BPSK over AWGN with Eb/N0, P_error = Q(√(2 Eb/N0)); then log10P_error = log10(Q(√(2 Eb/N0))).

Relation to related quantities: related to negative log-likelihoods, but specifically the log-base-10 of error probability; in log-scale, differences of 1 unit correspond to a factor of 10 in P_error.

See also: P_error, Q-function, log-likelihood.