Dual-mode decoding of product codes with application to tape storage

In this paper, we propose a dual-mode decoding technique for product codes in which the rows and columns may comprise either Reed-Solomon (RS) codewords or LDPC codewords. The first decoding mode uses standard hard-decision decoding algorithms on the rows and columns, after which a maximum-likelihood (ML) packet-erasure decoding algorithm is employed for the column code in a second decoding mode. For the second mode, the column code takes on a different character in which "slices" of the row code are treated as packets which are symbols in the column code. The ML decoder for this packet-level column code resolves the erroneous packets (erasures) flagged by the row code or a packet-level CRC code during the first decoding mode. By exploring an application to tape storage, we demonstrate that this dual-mode decoding method can dramatically improve the performance of a product code. Moreover, the complexity added by the second mode is manageable.