Rate-Adaptive Modulation and Low-Density Parity-Check Coding for Optical Fiber Transmission Systems

Abstract

We propose a rate-adaptive optical transmission scheme using variable-size constellations at a fixed symbol rate and variable-rate forward error correction (FEC) codes with soft-decision decoding (SDD), quantifying how achievable bit rates vary with transmission distance. The scheme uses outer Reed-Solomon codes and inner extended irregular repeat-accumulate low-density parity-check (LDPC) codes to vary the code rate, combined with single-carrier polarizationmultiplexed M-ary quadrature amplitude modulation with variable M and digital coherent detection. LDPC codes are decoded iteratively using belief propagation. Employing M = 4, 8, 16, the scheme achieves a maximum bit rate of 200 Gbit/s in a nominal 50-GHz channel bandwidth. A rate adaptation algorithm uses the signal-to-noise ratio (SNR) or the FEC decoder input bit-error ratio (BER) estimated by a receiver to determine the FEC code rate and constellation size that maximize the information bit rate while yielding a target FEC decoder output BER and a specified SNR margin. We simulate single-channel transmission through long-haul fiber systems with or without inline chromatic dispersion compensation, incorporating numerous optical switches, evaluating the impact of fiber nonlinearity and bandwidth narrowing. With zero SNR margin, we achieve bit rates of 200/100/50/20 Gbit/s over distances of 960/2800/4400/9680 km and 1920/4960/8160/19,360 km in dispersion-compensated and -uncompensated systems, respectively, corresponding to an increase of about 50% in reach compared to a reference system that uses a hard-decision FEC scheme. Compared to an ideal coding scheme, the proposed scheme exhibits a performance gap ranging from about 4.0 dB at 960 km to 2.7 dB at 9680 km in compensated systems, and from about 3.9 dB at 1920 km to 2.9 dB at 19,360 km in uncompensated systems. Observed performance gaps are about 2.5 dB smaller than for the reference hard-decision FEC scheme, close to the improvement expected when using SDD.

Rate-Adaptive Coded Modulation for Fiber-Optic Communications

“…In this figure, the AWGN capacity is plotted based on the Shannon formula, 2 log 2 (1 + SNR), for an AWGN channel for different transparent reaches. To this end, the SNR was estimated in two ways: analytically using the variance σ 2 Z x introduced for the Gaussian noise model and empirically by simulating at the output of the equalizer using a Monte-Carlo simulation in a similar way as in [30]. Fig.…”

“…Simulation results are provided for a 4D nonbinary LDPC CM scheme with probabilistic shaping over a non-DM PM single-channel fiber-optic link. According to the numerical results, the proposed scheme can operate within 2.7 dB from the AWGN capacity for bit rates between 178 Gb/s and 343 Gb/s, showing 1 dB performance improvement compared to [30]. Finally, the performance of the proposed system is compared with other rate-adaptive schemes in the literature as well as AWGN bounds.…”

“…The gap Δγ between γ and the minimum SNR obtained using the Shannon formula for an AWGN channel with the spectral efficiency η is a useful measure to compare different CM schemes 2 . This gap, referred to as gap from AWGN capacity [30], can be expressed as Δγ = γ − 10 log 10 (2 η − 1) dB.…”

“…To improve the utilization of optical networks with a dynamic or heterogeneous structure, we use the same approach as [30] to adapt the CM scheme to the CSI estimated by the receiver and reported back to the transmitter of the fiber-optic system. Similarly, we consider two choices for the CSI: (i) SNR, which is the symbol SNR estimated after polarization tracking and EDC, and (ii) the inner LDPC code performance, which is computed by a syndrome-based error estimator.…”

“…In a more practical scenario, a rate-adaptive scheme [30] is proposed exploiting six combinations of binary LDPC and RS codes together with three modulation formats. This scheme was capable of operating within 2.9 and 3.9 dB from the AWGN capacity in long and short non-DM single-channel fiber-optic links, respectively, showing 50% increase in transparent reach compared to the rate-adaptive system introduced in [31] with hard-decision FEC.…”