Low density parity check (LDPC) code is an attractive solution to improve data reliability while ensuring high speed data transmission in long haul optical communication systems. However, capacity approaching coding gains can be achieved only by employing extremely long binary LDPC codes. Non-binary LDPC codes provide same coding gain of binary LDPC codes with smaller codelength. But the decoding performance of these codes depends on the accurate realization of channel characteristics. All the existing works assume additive white Gaussian noise (AWGN) channel model for simplicity, which is not realistic. So mathematical analysis of photodetected signal is carried out and proved that the optical channel noise can be more efficiently modelled using chi-square distrubtion. Hence a non-binary quasi cyclic (NB QC) LDPC code based optical system with chi-square channel model is proposed for attaining large coding gains with smaller codeword lengths. Non-binary LDPC codes provide better error performance compared to their binary version while its quasi-cyclic property helps to reduce the encoding complexity. In order to reduce the decoding complexity, FFT based q-ary sum product algorithm is employed for LDPC decoding. The error performance analysis shows that the NB QC-LDPC codes with chi-square channel model gives more than 1dB coding gain than the AWGN channel model. The performance of the proposed system is also evaluated in terms of modulation schemes, data rates, dispersion effects and link distance. The results show that the NB QC-LDPC codes give better performace compared to their binary version for the proposed channel model.
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