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A novel electronic dispersion post-compensation algorithm is described and experimentally demonstrated for short reach optical links employing a directly modulated laser (DML) as a transmitter with subcarrier modulation (SCM) and digital signal processing enabled direct detection receiver. The proposed algorithm utilizes the functional relationship between the DML output optical power and chirp in deducing the received optical phase, which is normally lost under direct detection. Subsequently, standard frequency domain equalization is performed to mitigate the link dispersion. The proposed algorithm is applied to a single polarization 56 Gb/s and a dual polarization 112 Gb/s half-cycle Nyquist SCM signal transmitted over 4 km of single mode fiber. A 3 dB and 5 dB improvement in received optical power relative to the uncompensated system performance is achieved for the 56 Gb/s and 112 Gb/s signals at a bit error ratio of 1.0×10-3, respectively.