BSC Rate Feasibility Check

Problem

Return True when a rate is achievable on a binary symmetric channel with crossover probability p, that is when rate < 1 - H2(p). The binary entropy H2(p) is 0 when p equals 0 or 1.

Hint

Compute the capacity 1 - H2(p) and compare it strictly with the requested rate.

Test cases

case 1

in: [0.1,0.5]

expected: true

case 2

in: [0.1,0.6]

expected: false

case 3

in: [0,1]

expected: false

case 4

in: [0.5,0]

expected: false

case 5

in: [0.25,0.2]

expected: false

Starter codePython

import math
def bsc_rate_feasible(p, rate):
    # Your code here
    pass

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