Senior I Clinic Consultant Module:

Probability and Random Variables

• Sections B-1 through B-6, Couch,  pp. 634 - 649

• Consider a discrete, memoryless, binary channel with sent messages m₀ and m₁ and corresponding received messages are r₀and r_1. This channel has the following transitional probability characteristics: p(m₀) = 0.7, p(m₁) = 0.3, p(r₀\m₀) = 0.9, p(r₁\m₀) = 0.1, p(r₀\m₁) = 0.4 and p(r₁\m₁) = 0.6.
• Design an optimum-receiver algorithm for this channel.
• What is the probability for error for this channel?
• A discrete, memoryless, binary symmetric channel has a priori message probabilities, p₀ and p₁, for messages m₀ and m₁ respectively. The conditional error probability for channel transmission is p. The corresponding received messages are r₀ and r_1.
• Draw the transition probability diagram for this channel
• Calculate the probability of receiving r₀ and r₁
• Calculate the a posteriori probabilities p(m₀\r₀) and p(m₁\r₁).