Iterative Detection-Decoding of Interleaved Hermitian Codes for High Density Storage Devices

Traditionally, Reed-Solomon (RS) codes have been employed in magnetic data storage devices due to their effectiveness in correcting random errors and burst errors caused by thermal asperities and inter-symbol interference (ISI). However, as storage densities increase the effect of ISI becomes more severe and much longer RS codes are needed, but this requires significantly increasing the size of the finite field. A possible replacement for RS codes are the one-point Hermitian codes, which are a class of algebraic-geometric (AG) code that have larger block sizes and minimum Hamming distances over the same finite field. In this paper, we present a novel iterative soft detection-decoding algorithm for interleaved Hermitian codes. The soft decoding employs a joint adaptive belief propagation (ABP) algorithm and Koetter-Vardy (KV) list decoding algorithm. It is combined with a maximum a posteriori (MAP) partial response (PR) equalizer and likelihoods from the output of the KV or the ABP algorithm are fed back to the equalizer. The proposed scheme´s iterative detection-decoding behavior will be analyzed by utilizing the Extrinsic Information Transfer (ExIT) chart. Our simulation results demonstrate the performance gains achieved by iterations and Hermitian codes´ performance advantage over RS codes.