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Without being restrictive, optical signal propagation simulations performed in the case of a new concept of packet ring network pointed out that the Gaussian model is not sufficiently accurate to constitute a valuable model of noise-corrupted optical systems. This fact can be generalized to any common wavelength-division-multiplexing systems, using on-off keying transmissions where amplified spontaneous emission is the main noise source. In this letter, we propose an alternative chi-square model, which is more accurate and corrects deficiencies of the Gaussian model. In such specific channel, we design an error-correcting scheme based on low-density parity check (LDPC) codes associated to soft decoding. The performance of a chi-square-based LDPC soft decoder and a Gaussian-based one are compared, both applied to a real chi-square optical channel. We point out that the design can be done assuming an additive white Gaussian noise statistic but also that considering the real channel statistics is essential to achieve optimal performance.