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In this study, the authors propose an exact maximum likelihood (ML) signal-to-noise ratio (SNR) estimator for coded linearly modulated signals. The estimator is expressed in terms of the marginal a posteriori probabilities (APPs) of the coded symbols, which can be obtained efficiently by the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm for codes defined on trellises. Simulation results show that the proposed ML code-aided (CA) SNR estimator significantly outperforms the non-data-aided (NDA) estimators in the low SNR regime. The Cramer-Rao bound (CRB) for CA SNR estimator is also derived and evaluated numerically. It is shown that the proposed ML-CA estimator performs very close to the derived bound. Comparisons of the CRBs for CA and NDA scenarios with different linearly modulated signals further illustrate the intrinsic performance improvement by exploiting the channel coding constraints.