The document discusses a binary digital communication channel that transmits bits perturbed by Gaussian noise, leading to potential errors in reception. It defines sent signals and received symbols, along with their respective probabilities. It suggests using Bayes' formula to find the a posteriori probabilities of the transmitted bits based on the observed signals.

1. 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 O 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 O 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)