Motivated by the classical synchronization problem and emerging applications in bioinformatics, we study noisy deletion channels in a regime of practical interest: short code length, low decoding complexity and low SNR. Our work is inspired by an important insight from information theory and Markov chains: appropriately parametrized Markov codewords can correct deletions and errors (due to noise) simultaneously. We extend this idea to practice by developing a low complexity decoder for short Markov codes, which displays competitive performance in simulations at low SNRs. Our decoder design combines the sequence prediction capability of recurrent neural networks with the assured performance of maximum a posteriori (MAP) decoders like the BCJR decoder. © 2020 IEEE.