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In this paper, regular low-density parity-check (LDPC) codes have been applied for the first time to a low cost spectrum-sliced WDM system. The Gaussian approximation of the noise in such system has been commonly used in previous studies, and there is a standard LDPC code for symmetric additive white Gaussian noise (AWGN) channels. However, in the system considered here the actual noise character is asymmetric and chi-square distributed. Due to the specific channel property, an adaptive decoding algorithm based on the precise chi-square noise statistics has been proposed. Simulations are conducted for various code rates. The results show that such a forward error correction scheme provides significant coding gain for a dedicated system and the adaptive algorithm outperforms decoding with conventional Gaussian approximations.