1. A data processing system, the data processing system comprising: a data detector circuit operable to apply a data detection algorithm to a data input to yield a first detected output, and to apply the data detection algorithm to the data input guided by a first decoded output to yield a second detected output; and a data decoder circuit operable to: apply a first data decoding algorithm to the first detected output to yield the first decoded output; and apply a second data decoding algorithm to the second detected output to yield a second decoded output.