Capacity-achieving symbol distributions for directly modulated laser and direct detection systems

Abstract

We investigate the capacity-achieving symbol distributions for directly modulated laser (DML) and direct-detection (DD) systems utilizing probabilistic constellation shaped pulse amplitude modulation formats. DML-DD systems utilize a bias tee to feed the DC bias current and AC-coupled modulation signals. Also, an electrical amplifier is commonly utilized to drive the laser. Thus, most DML-DD systems are subject to the constraints of the average optical power and peak electrical amplitude. We compute the channel capacity of the DML-DD systems under these constraints by using the Blahut-Arimoto algorithm to obtain the capacity-achieving symbol distributions. We also carry out experimental demonstration to verify our computation results. We show that the probabilistic constellation shaping (PCS) technique marginally increases the capacity of DML-DD system when the optical modulation index (OMI) is less than 1. However, the PCS technique allows us to increase the OMI larger than 1 without clipping distortions. As a result, we can increase the capacity of DML-DD system by using the PCS technique in comparison with the uniformly distributed signals.