An entropy maximization problem related to optical communication

Finding a g that will minimize Ps (g) will involve a detailed study of the function v,(g). We conjecture that in general the best encoder g, will outperform the best linear encoder G,. Unfortunately, PPM is characterized by a large peak-to-average power ratio requirement: for Mary PPM the needed ratio is exactly M. If the optical power source is a semiconductor laser, it is difficult to achieve such large values of the peak-to-average power ratio. One possible way to reduce this ratio while at the same time maintaining energy efficiency is to use more than one optical frequency (color). In fact, if N distinguishable colors are used with M-ary PPM, then for a model similar to that in [lo] the channel capacity is log(M) + log(N) nat/photon with a peakto-average power ratio of M. For example, the proposed monochromatic NASA system is in principle equivalent to a 16-color 16-ary PPM system whose peak-to-average power ratio is only 16, instead of 256.