In digital communication receivers, ambiguities in terms of timing and phase need to be resolved prior to data detection. In the presence of powerful error-correcting codes, which operate in low signal-to-noise ratios (SNR), long training sequences are needed to achieve good performance. In this contribution, we develop a new class of code-aided ambiguity resolution algorithms, which require no training sequence and achieve good performance with reasonable complexity. In particular, we focus on algorithms that compute the maximum-likelihood (ML) solution (exactly or in good approximation) with a tractable complexity, using a factor-graph representation. The complexity of the proposed algorithm is discussed and reduced complexity variations, including stopping criteria and sequential implementation, are developed.