MI from LLRs

Problem

Estimate the mutual information in bits from a list of nonnegative LLR samples using the standard J-function style estimator:

I = 1 - mean(log2(1 + exp(-L_i)))

Assume every sample is nonnegative and the list is non-empty.

Hint

Zero LLRs mean the observations carry no information about the bits.

case 1

in: [[0,0]]

expected: 0

case 2

in: [[1,2,3]]

expected: 0.7649479245566632

case 3

in: [[0.5,1.5,2.5]]

expected: 0.6372199067226494

case 4

in: [[10,10]]

expected: 0.999934503233238

Starter codePython

import math
def mi_from_llrs(llrs):
    # Your code here
    pass

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