This contribution deals with two hypothesis testing problems for digital receivers: frame synchronization and phase ambiguity resolution. As current receivers use powerful error-correcting codes and operate at low signal-to-noise ratio (SNR), these problems have become increasingly challenging: one is forced either to waste a part of the bandwidth on training symbols or to consider novel hypothesis testing techniques. We will consider five algorithms for hypothesis testing that exploit properties of the underlying channel code: a re-encoding (REEN) technique, an algorithm we previously derived from the expectation-maximization (EM) algorithm, two recently proposed algorithms known as mode separation (MS) and pseudo-ML (PML), and a technique where all hypotheses are tested simultaneously by applying the sum-product algorithm (SPA) to the overall factor graph of the system. These techniques will be compared in terms of their computational complexity, the class of problems to which they can be applied and their error rate performance. Through computer simulations we show that the EM-based and the PML algorithms have excellent performance. The MS, PML, REEN, and EM-based algorithms all have similar complexity, but the latter algorithm is suitable for a much wider range of applications. The SPA has the lowest computational complexity, but might yield poor performance