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.