(a) A binary communication channel carries data as one of two sets of signal denoted by...

 

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(a) A binary communication channel carries data as one of two sets of signal denoted by '0' and '1'. Due to the noise on the channel, a '0' can be received as 'I' and vice-versa. For a given channel, it can be assumed that a transmitted '0' is correctly received with probability 0.95, and transmitted '1' is correctly received with probability of 0.75. Also, 70% of all messages are transmitted as a '0'. If a signal is sent, answer that following questions: (i) Determine the probability that 'I' was received. [5 marks] (ii) If 'I' was received, determine the probability that '1' was transmitted. [5 marks] (b) The voice signal in a PCM system is quantized in 16 levels with the following probabilities: P = P P P = 0.1 Ps P, P, P = 0.05 P = P10 P = P = 0.075 P3 P4 Pis P16 = 0.025 Assume f = 3 kHz. (i) Determine the entropy. (ii) Determine the information rate. [5 marks] [5 marks] (a) A binary communication channel carries data as one of two sets of signal denoted by '0' and '1'. Due to the noise on the channel, a '0' can be received as 'I' and vice-versa. For a given channel, it can be assumed that a transmitted '0' is correctly received with probability 0.95, and transmitted '1' is correctly received with probability of 0.75. Also, 70% of all messages are transmitted as a '0'. If a signal is sent, answer that following questions: (i) Determine the probability that 'I' was received. [5 marks] (ii) If 'I' was received, determine the probability that '1' was transmitted. [5 marks] (b) The voice signal in a PCM system is quantized in 16 levels with the following probabilities: P = P P P = 0.1 Ps P, P, P = 0.05 P = P10 P = P = 0.075 P3 P4 Pis P16 = 0.025 Assume f = 3 kHz. (i) Determine the entropy. (ii) Determine the information rate. [5 marks] [5 marks]