Z-Channel Capacity

Problem

Return the capacity in bits of a Z-channel with crossover q, where a transmitted 1 is flipped to 0 with probability q and a 0 is never flipped:

C = log2(1 + (1 - q) * q^(q / (1 - q)))

Return 1.0 for q <= 0 and 0.0 for q >= 1.

Hint

The optimal input distribution for a Z-channel is not uniform.

case 1

in: [0]

expected: 1

case 2

in: [0.5]

expected: 0.32192809488736235

case 3

in: [0.1]

expected: 0.7628482520105094

case 4

in: [0.25]

expected: 0.5582386267373455

case 5

in: [0.9]

expected: 0.05483743386065755

Starter codePython

import math
def z_channel_capacity(q):
    # Your code here
    pass

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