Question

A binary digital communication channel transmits a sequence of 0 's and 1 's. Each symbol/bit in the Q4 sequence is perturbed independentiy by Gaussian noise so that, in some cases, errors occur; that is 1 is recelved as 0 or a 0 as a 1. Let the sent signais 1 and O be designated by B3​ abd B2​, respectively, the recelved symbols 1 and 0 by A1​ and A2​. Let the a priori probability that a 1 or a 0 was sent be given by p and q, respectively. Find the a posteriori probabilities P(B1​/Ak​) where j and k=1,2. (Hint: Use Bayes' Formula)

Answer 1

A posteriori probabilities are conditional probabilities that are calculated based on prior knowledge and new data. We can use Bayes' Formula to calculate these probabilities.

Step-by-step explanation:

A posteriori probabilities are conditional probabilities that are calculated based on prior knowledge and new data. In this case, we want to find the probabilities that a 1 or a 0 was sent given the received symbols A1​ and A2​.

We can use Bayes' Formula to calculate these probabilities.

Bayes' Formula states that the probability of an event A occurring given that event B has occurred is equal to the probability of both A and B occurring divided by the probability of event B occurring.

To calculate the a posteriori probability P(B1/A1), we can use the formula:

P(B1/A1) = (P(A1/B1) * P(B1)) / P(A1)

Similarly, to calculate the a posteriori probability P(B1/A2), we can use the formula:

P(B1/A2) = (P(A2/B1) * P(B1)) / P(A2)