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 symbolpair 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.
The performance of LDPC codes decoded by iterative algorithms depends on the structural properties of their underlying Tanner graphs. For general memoryless channels, error patterns dominating the bit and frame error probabilities at the error floor region are termed trapping sets. In this paper, we propose an effective method for finding small-size trapping sets of LDPC codes. In the proposed method, a probabilistic algorithm to find low-weight codewords is applied to finding small trapping sets of LDPC codes. Furthermore, we show numerical results of examining small trapping sets of (504, 252) and (1008, 504) LDPC codes.
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