MI of Gaussian Channel

Problem

Compute the mutual information in bits between an input X ~ N(0, power) and the output Y = X + N with independent noise N ~ N(0, noise_var):

I = 0.5 * log2(1 + power / noise_var)

Hint

Quadrupling the signal-to-noise ratio adds 1 bit.

case 1

in: [1,1]

expected: 0.5

case 2

in: [3,1]

expected: 1

case 3

in: [15,1]

expected: 2

case 4

in: [1,4]

expected: 0.16096404744368117

Starter codePython

import math
def gaussian_channel_mi(power, noise_var):
    # Your code here
    pass

4 test cases · run your code against them in the editor