161-A5.1

In this module, you have learned that it is possible to synthesize extremal channels from multiple copies of a given binary-input channel. In particular, the binary erasure channel (BEC) has the property that all synthesized channels are equivalent to BECs.

Task Description

Your task in Module 5 is simple: given the erasure probability $p$ of a BEC, you are to count the number of synthetic channels with erasure probability that is better (lower) than the original BEC.

You need to write a function count_bad_channels which will take two arguments:

• blocklength - an int that is a power of two, denoting the blocklength or, equivalently, the number of synthetic channels produced via the polar transform.
• erasure_prob - a float, a positive real number between 0 and 1, indicating the erasure probability of the original BEC.

The function must return an int corresponding to the number of synthetic BECs with erasure probabilities strictly less than erasure_prob.

Python test script for execution

Header	import math
Student submission (function only)	def count_bad_channels(blocklength, erasure_prob): # your code.. # more code.. return ans }
Main test script	# Main test script goes here, and will not be visible to students. # The script will test if the submitted code does the prescribed functionality. # For successfully validated scripts, test results will be sent via email.

Expected Output

	$n=2$	$n=4$	$n=16$	$n=256$	$n=65536$
$\epsilon =0.1$	1	1	4	39	7291
$\epsilon =0.3$	1	1	6	86	20158
$\epsilon =0.8$	1	3	11	193	51758