Decoding Correlated Received Multi-Symbol Data by Guessing Noise Effect

Methods for correcting errors arising in correlated received multi-symbol data by guessing noise effects at a receiver device are disclosed. In various embodiments, the ordering of symbol-level noise effects is informed by correlated soft information. A lattice of possible joint combinations of interfering symbols and/or symbols impacted by correlated noise is constructed. Then, determining a decoded codeword includes iteratively guessing new noise effects expressed as a set of lattice-point substitutions over a multi¬ symbol data block, and checking whether the data associated with the resultant lattice points form a codeword using a codebook membership function. In some embodiments, the decoder is restricted to testing a constrained collection number of lattice points and can abandon searching and declaring an erasure.