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Regular low-density parity-check (LDPC) codes have been applied for the first time to a low-cost spectrum-sliced wavelength division multiplex system. The Gaussian approximation of the noise in such system has been commonly used in previous studies, and there is a standard LDPC for symmetric additive white Gaussian noise channels. However, in the system considered here, the actual noise character is asymmetric and is chi-square distributed. Owing to the specific channel property, an adaptive decoding algorithm based on the precise chi-square noise statistics has been proposed and proved to outperform decoding with conventional Gaussian approximations. 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 in terms of improving the overall transmission capacity and available power budget.