Capacity of Cascaded Erasure Channels

Problem

Two binary erasure channels with erasure probabilities e1 and e2 are used in series. Return the capacity in bits of the equivalent erasure channel, 1 - e with e = e1 + e2 - e1*e2. Assume e1 and e2 lie in [0, 1].

Hint

An erasure survives only if neither stage erases it, which gives the combined probability.

Test cases

case 1

in: [0.1,0.2]

expected: 0.72

case 2

in: [0,0.5]

expected: 0.5

case 3

in: [1,0.5]

expected: 0

case 4

in: [0,0]

expected: 1

case 5

in: [0.3,0.3]

expected: 0.49

Starter codePython

def cascaded_bec_capacity(e1, e2):
    # Your code here
    pass

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