Abstract-Codes on graphs of interest for next generation forward error correction (FEC) in high-speed optical networks, namely turbo codes and low-density parity-check (LDPC) codes, are described in this invited paper. We describe both binary and nonbinary LDPC codes, their design, and decoding. We also discuss an FPGA implementation of decoders for binary LDPC codes. We then explain how to combine multilevel modulation and channel coding optimally by using coded modulation. Also, we describe an LDPC-coded turbo-equalizer as a candidate for dealing simultaneously with fiber nonlinearities, PMD, and residual chromatic dispersion.

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Abstract-We study a turbo equalization scheme based on low-density parity-check (LDPC) coded turbo equalization (TE). This scheme is suitable for simultaneous: (i) suppression of intrachannel nonlinearities, (ii) chromatic dispersion compensation, and (iii) polarization-mode dispersion (PMD) compensation. LDPC coding is based on large girth (g ≥ 8) block-circulant codes, and maximum a posteriori probability (MAP) equalizer is based on Bahl-Cocke-Jelinek-Raviv (BJCR) algorithm. The ultimate channel capacity limits, assuming an independent identically distributed (i.i.d.) source are reported as well. In the presence of intrachannel nonlinearities the LDPC-coded TE provides almost 12 dB improvement over BCJR equalizer at BER of 10 −8 . For an NRZ system operating at 10 Gb/s with residual dispersion of 11200 ps/nm and for differential group delay of 50 ps, the LDPC-coded TE is only 1 dB away from the i.i.d channel capacity. The efficiency of LDPC-coded TE in PMD compensation is demonstrated experimentally, with decoding performed off line.

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Large-girth quasi-cyclic LDPC codes have been experimentally evaluated for use in PMD compensation by turbo equalization for a 10 Gb/s NRZ optical transmission system, and observing one sample per bit. Net effective coding gain improvement for girth-10, rate 0.906 code of length 11936 over maximum a posteriori probability (MAP) detector for differential group delay of 125 ps is 6.25 dB at BER of 10(-6). Girth-10 LDPC code of rate 0.8 outperforms the girth-10 code of rate 0.906 by 2.75 dB, and provides the net effective coding gain improvement of 9 dB at the same BER. It is experimentally determined that girth-10 LDPC codes of length around 15000 approach channel capacity limit within 1.25 dB.

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