In this paper, we present a reduced-latency nonbinary low-density parity-check (LDPC) coded modulation scheme suitable for high-speed optical fiber communication featuring the layered LDPC decoding algorithm. The use of the layered decoder in place of the conventional flooding decoder helps reduce by half the number of iterations taken in decoding. This in turn reduces the decoding latency, increases the decoding throughput, and significantly lowers the power consumption at the receiving ends of optical transport networks. We show by using the experimental data collected from a 4-ary rate-0.8 LDPC-coded NRZ-DQPSK modulation system that layered decoding indeed halves the required number of decoding iterations. We also show that, in the back-to-back configuration, even with a single iteration of layered decoding, one can attain a 7 dB gain in performance at the bit error ratio (BER) of 10-5 when compared to using only the maximum a posteriori probability detector output based on the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm.