Z-Channel Mutual Information

Problem

Compute I(X;Y) in bits for a Z-channel where P(X = 1) = px1 and a 1 is flipped to 0 with probability q while a 0 is never flipped. With py1 = px1 * (1 - q):

I = H(py1) - px1 * H(q)

where H is the binary entropy function in bits.

Hint

Only inputs of 1 can be corrupted, so H(Y|X) = px1 * H(q).

Test cases

case 1

in: [0.5,0]

expected: 1

case 2

in: [0.5,0.5]

expected: 0.31127812445913283

case 3

in: [1,0.2]

expected: 0

case 4

in: [0.9,0.1]

expected: 0.27937542565354423

Starter codePython

import math
def z_channel_mi(px1, q):
    # Your code here
    pass

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