On the Capacity Region of the Intensity-Modulation Direct-Detection Optical Broadcast Channel

The capacity of the intensity-modulation direct-detection free-space optical broadcast channel (OBC) is investigated. The Gaussian model with input-independent Gaussian noise is used, with both average and peak intensity constraints. An outer bound on the capacity region is derived by adapting Bergmans’ approach to the OBC. Inner bounds are derived by using superposition coding with either truncated-Gaussian distributions or discrete distributions. While the discrete input distribution achieves higher rates than the truncated-Gaussian distribution, the latter allows expressing the achievable rate region in a closed form. At high signal-to-noise ratio (SNR), it is shown that the truncated-Gaussian distribution is nearly optimal. It achieves the symmetriccapacity within a constant gap (independent of SNR), which approaches half a bit as the number of users grows large. It also achieves the capacity region within a constant gap, which depends on the number of users. At low SNR, it is shown that on-off keying with time-division multiple-access (TDMA) is optimal, as it achieves any point on the boundary of the developed outer bound. This is interesting in practice since both OOK and TDMA have low complexity. At moderate SNR (typically [0, 8] dB), a discrete distribution with a small alphabet size achieves a fairly good performance in terms of symmetric rate.