A system including a detection module, a reconstruction module, and a correlation module. The detection module receives first signals from a medium and detects data bits from the first signals. The reconstruction module reconstructs the data bits and generates second signals. The correlation module generates first correlation values by correlating the first and second signals and generates second correlation values by self-correlating the second signals. In response to at least one of the first and second signals including a floating number having a plurality of bits and a sign bit, the correlation module generates at least one of the first and second correlation values based on a plurality of most significant bits of the floating number and the sign bit of the floating number. The first and second correlation values indicate whether the data bits detected from the first signals include errors due to defects in the medium.