A data storage device for storing N-symbol codewords. The device implementing a method including: reading q-level memory cells to obtain a read signal having N signal components; detecting the memory cell level corresponding to each component using a first correspondence criterion dependent on reference signal levels; identifying unreliable components; detecting, for each unreliable component, the next-most-closely corresponding memory cell level according to the first correspondence criterion; defining a set of ordered codeword vectors having N symbols corresponding to respective components of the read signal ordered according to a signal level, wherein the symbol values in each ordered codeword vector correspond to one combination of detected memory cell levels; defining, for each read signal, candidate initial vectors having intersected the ordered codeword vectors and plurality of initial vectors; and detecting, if the candidate initial vectors contains a vector, the codeword corresponding to that read signal that depends on the candidate initial vectors.