BEC Mutual Information

Problem

Compute the mutual information in bits of a binary erasure channel with erasure probability pe when the input is 1 with probability px1. The formula is I = (1 - pe) * H(px1), where H is the binary entropy function in bits; degenerate inputs with px1 = 0 or 1 carry no information.

Hint

Erasures only scale the information down by the fraction of symbols that arrive.

Test cases

case 1

in: [0.5,0]

expected: 1

case 2

in: [0.5,0.5]

expected: 0.5

case 3

in: [0.25,0.2]

expected: 0.6490224995673063

case 4

in: [1,0.3]

expected: 0

Starter codePython

import math
def bec_mutual_information(px1, pe):
    # Your code here
    pass

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