Linear programming decoding of binary linear codes for symbol-pair read channel

In this study, we develop a new algorithm for decoding binary linear codes for symbol-pair read channels. The symbol-pair read channel was recently introduced by Cassuto and Blaum to model channels with higher write resolutions than read resolutions. The proposed decoding algorithm is based on linear programming (LP). For LDPC codes, the proposed algorithm runs in time polynomial in the codeword length. It is proved that the proposed LP decoder has the maximum-likelihood (ML) certificate property, i.e., the output of the decoder is guaranteed to be the ML codeword when it is integral. We also introduce the fractional pair distance d_{f p} of the code, which is a lower bound on the minimum pair distance. It is proved that the proposed LP decoder corrects up to d_{f p} =2 - 1 errors.