A tensor-product parity code for magnetic recording

In magnetic recording, a standard code architecture consists of an outer Reed–Solomon code in concatenation with an inner parity code. The inner parity code is used to detect and correct common error events. Generally, a parity code with short block length performs better, as multiple error events within one block and, consequently, miscorrection are less likely. In this paper, we study an inner code that offers the same system performance as a parity code with very short block length, even as short as the symbol length (in bits) of the outer Reed–Solomon code, but with higher code rate. This code is a tensor-product code, with a Bose–Chauduri–Hocquenghem (BCH) code and a short parity code as constituent codes. The decoder for this code is not much more complex than the optimal decoder of the baseline parity-coded channel; in fact, the only additional steps are Viterbi detection matched to the channel and decoding of the BCH code. Index Terms—BCH code, magnetic recording, parity code, Reed–Solomon code, tensor-product code. I