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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 polarization-multiplexed 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 SD- .