Wyner-Ziv Gaussian Rate

Problem

Return the Wyner-Ziv rate in bits for a Gaussian source with side information:

R = 0.5 * log2(var * (1 - rho^2) / distortion)

where rho is the correlation with the side information at the decoder. Assume 0 < distortion <= var * (1 - rho^2).

Hint

Stronger side information reduces the conditional variance and the rate.

case 1

in: [1,0,0.25]

expected: 1

case 2

in: [1,0.5,0.75]

expected: 0

case 3

in: [4,0,1]

expected: 1

case 4

in: [4,0.6,2]

expected: 0.17807190511263768

Starter codePython

import math
def wyner_ziv_gaussian_rate(var, rho, distortion):
    # Your code here
    pass

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