Syndrome decoding of symbol-pair codes

Cassuto and Blaum proposed new error correcting codes which are called symbol-pair codes. They gave a coding framework for channels whose outputs are overlapping pairs of symbols in storage applications. It is called symbol-pair read channel. The pair distance and pair error are used in symbol-pair read channel. Cassuto et al. and showed Yaakobi et al. presented decoding algorithms for symbol-pair codes. However, their decoding algorithms cannot always correct errors whose number is not more than half the minimum pair distance. In this paper, we propose a new decoding algorithm using the syndrome of symbol-pair codes. In addition, we show that the proposed algorithm can correct all pair errors within the pair error correcting capability.