Practical iterative decoding scheme using Reed-Solomon codes for magnetic recording channels

The short-term iterative decoding implementation proposed in this paper not only uses conventional long-distance Reed-Solomon codes (RS codes), but also uses short-distance RS codes consisting of redundant symbols P and Q periodically inserted into the data in 512-byte sectors. A single parity matrix composed of redundant symbol P is decoded by using a belief propagation algorithm (BPA) such as low density parity check (LDPC) decoding. The Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm is used for EEPR4 channel decoding. Serial iterative decoding is done by using log likelihood ratios produced by both algorithms. Simulations of the use of 28 redundant symbols of the short-distance RS codes and 30 symbols of the long-distance RS codes have confirmed that at a block error rate of about 10^-1 (bit-error rate) ≈10^-3 the proposed system can reduce the block error rate more than tenfold. Consequently, one block erasure correction including 30 symbols per sector can be achieved at the same error rate.