Question

Suppose the probability of transmitting a single digit incorrectly is greater than 0.5. Explain why "inverse decoding" (decoding 1 as 0 and 0 as 1) should be employed.

Short answer

If the probability of transmitting a single digit incorrectly is greater than 0.5, then if we decode 0 as 1 and 1 as 0, we have a high chance to decode messages correctly so inverse decoding should be employed.

Step-by-step solution

Inverse decoding

It is a decoding technique in which 1 is decoded as 0 and zero is decoded as 1.

Explaining why inverse decoding should be employed

Since the probability of transmitting a single digit incorrectly is greater than 0.5, this implies the probability of transmitting a single digit correctly is less than 0.5.

Since the probability of transmitting the correct digit is less than the probability of transmitting an incorrect digit. So, if we decode 0 as 1 and 1 as 0, we have a high chance to decode messages correctly so inverse decoding should be employed.

Hence if the probability of transmitting a single digit incorrectly is greater than 0.5, then inverse decoding should be employed.