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This paper considers the design of capacity-approaching, non-uniform optical intensity signalling in the presence of average and peak amplitude constraints. Although it is known that the capacity achieving input distribution is discrete with a finite number of mass points, finding it requires complex non-linear optimization at every SNR. In this paper, a simple expression for a capacity-approaching distribution is derived via source entropy maximization. The resulting mutual information using the derived discrete non-uniform input distribution is negligibly far away from the channel capacity. The computation of this distribution is substantially less complex than previous optimization approaches and can be easily computed at different SNRs.
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