Motivated by emerging applications in bioinformatics and other applications of synchronization channels, we study noisy deletion channels in a regime of practical interest: short code length, low decoding complexity, and low SNR. Deletion channels have been of interest to information theorists for a long time. Finding a good code for these channels, which can detect positions of deletions and correct them efficiently, has proven to be very hard. There has been a lot of work on fixed and random deletion channels and research is still going on. In parallel, another line of research is for finding capacity of deletion channels. Though there exist some upper and lower bounds for capacity of i.i.d deletions, the actual capacity expression is still unknown. 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. Through experiments we show the performance of neural network based decoders
for Markov codes over noisy channels, deletion channels and other synchronization channels.