The effect of Kerr-induced optical fiber nonlinearities in C-band (5 THz) EDFA and C+L-band (12.5 THz) Raman-amplified optical communication systems has been studied considering the impact of third-order fiber dispersion. The performance of digital nonlinearity compensation with single channel and 250-GHz bandwidth in both EDFA and Raman amplified systems has been investigated, respectively. The achievable information rates (AIRs) and optimum code rates in each individual transmission channel have been evaluated for the DP-64QAM, the DP-256QAM and the DP-1024QAM modulation formats, both with and without the use of the probabilistic shaping technique. It is found that, for all considered modulation formats, the signal-to-noise ratios, AIRs and code rates exhibit significantly asymmetric behavior about the central channel due to the presence of the third-order dispersion. This provides a new insight that the forward error correction schemes have to be optimized asymmetrically, on a per-channel basis, to maximize the overall throughput.