Devices and methods described herein decode a sequence of coded symbols by guessing noise. In various embodiments, noise sequences are ordered, either during system initialization or on a periodic basis. Then, determining a codeword includes iteratively guessing a new noise sequence, removing its effect from received data symbols (e.g. by subtracting or using some other method of operational inversion), and checking whether the resulting data are a codeword using a codebook membership function. In various embodiments, soft information is used to generate a symbol mask that identifies the collection of symbols that are suspected to differ from the channel input, and only these are subject to guessing. This decoder embodies or approximates maximum likelihood (optionally with soft information) decoding for any code. In some embodiments, the decoder tests abounded number of noise sequences, abandoning the search and declaring an erasure after these sequences are exhausted.