RegionPlot in Shannon capacity theorem?

Questions
,
1

The Shannon Capacity Theorem identifies the limits of performance for bandwidth-limited and power-limited Gaussian channels.

In log-form, the theorem is defined by the following equation:

log-form.png

In exponential form, the Capacity equation is:
exponential-form.png

In locus-of-points form, the equation states that the Capacity Boundary is the locus of all points given by the following equation:
locus-of-points-form.png

The attached figure shows the Capacity Boundary. The region below the curve is referred to as the “feasible” region. The region above the curve is referred to as the “infeasible” region. As shown in the figure, the capacity is plotted on a Log-Linear graph.

shannon-graph.png
shannon-graph.png490×249 40.4 KB

I would like recommendations of how to perform a RegionPlot of the Log-Linear graph. I would like the see to RegionPlot the both below the curve and above the curve in two different color shades.

I have attached a copy of the program that I used to generate the graph.

Open in Wolfram Cloud ↗
2

Hi Edward,

Is there a reason for wanting to use RegionPlot? How about this?

p1 = ListLogPlot[t6,
  GridLines -> {xgrid, ygrid},
  Joined -> True,
  Frame -> True,
  PlotLegends -> {"Shannon_Limit"},
  PlotStyle -> {Blue},
  FrameLabel -> {"\!\(\*FractionBox[\(Eb\), \(N0\)]\)dB",  "Spectrum Efficiency -- bit/sec/Hz"},
  GridLinesStyle -> {Directive[Thick, Black]},
  FrameTicks -> {{Automatic, Automatic}, {xticks, Automatic}},
  FrameStyle -> Directive[Bold],
  LabelStyle -> Directive[Black, Bold, 12],
  Filling -> {1 -> Top, 1 -> Bottom},
  FillingStyle -> {Directive[Opacity[0.25], Red], Directive[Opacity[0.25], Green]}]

10658plot.png
10658plot.png614×299 15.9 KB

You may also want to check the documentation for HatchFilling.

3

Hi Rohit:

Thanks. This is exactly what I had hope to accomplish. No, there was no particular reason to use RegionPlot, other than, I thought it was the appropriate method. And per you recommendation, I did investigate HatchFilling. For the future, I now have two more approaches in my toolbox. Again thanks.