This article presents the novel FPGA-based 1 Gb/s near-Shannon-limit ACM modem developed within the MHOMS program with particular focus on the advanced modem algorithm solutions devised. A number of powerful FEC schemes have been analyzed as possible candidates for the MHOMS modem, and the final selection is justified in terms of the best tradeoff between complexity and performance. State-of-the-art modulation and demodulation algorithms are also presented, including nonlinearity dynamic precompensation techniques and innovative synchronization strategies required by the selected powerful modulation and coding schemes. Overall modem performances are also shown for a variety of spectral efficiencies.