Suppose three digital data values [-1, 0, +1] are transmitted across a noisy cha

Question

Suppose three digital data values [-1, 0, +1] are transmitted across a noisy channel. The probability that digital data 0 input is transmitted is p (0) = 1/4 The probability that digital data 1 input is transmitted is p (1) = 1/4. The probability that digital data -1 input is transmitted is p [-1] = 1/2, According to the transition error probability channel shown below. A digital data 1 input is transmitted (to 1 output) with error probability P (epsilon_1) = 0.20 A digital data 0 input is transmitted (to 0 output) with error probability P (epsilon_0) = 0.15 A digital data -1 input is transmitted (to -1 output) with error probability, P (epsilon_-1) = 0.25. What is the probability of a channel error of digital data? If I observe a digital data error at the output, What is the probability that a digital-1 was the digital input data.

Explanation / Answer

a) probaility of channel error = sum of probablites of a digital input multiplied by their probaility

= p(0)p(e0)+p(1)p(e1)+p(-1)p(e-1)= (1/4 * 0.15)+ (1/4 * 0.20) + (1/2 * 0.25 )

= 0.2125

b) this is a condiional probability , given that there is a error at the output what is the probability its -1 = p(e-1 | channel error) = p(e-1 intersection channel error)/ prob of channel error

=p(-1)p(e-1)/p(channel error)

= (1/2*0.25) / p(channel error)

= 0.125/ (answer of part a) = 0.125 / 0.2125 = 0.5882

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.