Capacity of the Poisson Channel with Random Noise Intensity
NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS
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An upper bound B sub f is given for the information capacity of the Poisson channel with marginally stationary random noise intensity and causal feedback. The capacity is shown to converge to B sub f in the limit of longer and longer communication intervals for a class of random noise intensities including the case in which the noise intensity is nontime-varying. An upper bound B sub nf on the capacity is also established for the Poisson channel with marginally stationary noise and no feedback. In this case also, for a class of random noise intensities including nontime-varying noise intensity, B sub nf is found to be the capacity of the channel without feedback in the limit of longer and long communication intervals. The fractional difference between B sub f and B sub nf is considered as a means to quantify the improvement afforded by feedback. Also, certain nonstandard encoder constraints are addressed and the importance of the encoder intensity peak constraint to the channel capacity problem is explored.