1. A data storage device comprising: a non-volatile memory; and a controller coupled to the non-volatile memory, wherein the controller includes a decoder configured to perform a decoding operation using codeword data read from the non-volatile memory, wherein the decoder includes: syndrome storage; a first barrel shifter configured to bit-shift hard decision bit data to generate shifted data that is aligned with a set of syndromes from the syndrome storage; and a first syndrome update circuit coupled to the first barrel shifter and configured to process the set of syndromes based on the shifted data to generate an updated version of the set of syndromes.