1. A data processing system, the data processing system comprising: a first data decoding circuit operable to apply a low density parity check decoding algorithm to a decoder input to yield a first decoded output; and a second data decoding circuit coupled to the first data decoding circuit and a data output circuit, wherein the second data decoding circuit is operable to apply a finite alphabet iterative decoding algorithm to the first decoded output to yield a second decoded output, and wherein the second decoded output is only provided to one or both of the data output circuit or the second data decoding circuit.