Achievable Information Rates for Coded Modulation With Hard Decision Decoding for Coherent Fiber-Optic Systems

We analyze the achievable information rates (AIRs) for coded modulation schemes with quadrature amplitude modulation constellations with both bitwise and symbolwise decoders, corresponding to the case where a binary code is used in combination with a higher order modulation using the bit-interleaved coded modulation (BICM) paradigm and to the case where a nonbinary code over a field matched to the constellation size is used, respectively. In particular, we consider hard decision decoding, which is the preferable option for fiber-optic communication systems where decoding complexity is a concern. Recently, Liga et al. analyzed the AIRs for bitwise and symbolwise decoders considering what the authors called hard decision decoder, which, however, exploits soft information of the transition probabilities of discrete-input discrete-output channel resulting from the hard detection. As such, the complexity of the decoder is essentially the same as the complexity of a soft decision decoder. In this paper, we analyze instead the AIRs for the standard hard decision decoder, commonly used in practice, where the decoding is based on the Hamming distance metric. We show that if standard hard decision decoding is used, bitwise decoders yield significantly higher AIRs than the symbolwise decoders. As a result, contrary to the conclusion by Liga et al., binary decoders together with the BICM paradigm are preferable for spectrally efficient fiber-optic systems. We also design binary and nonbinary staircase codes and show that, in agreement with the AIRs, binary codes yield better performance.