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For the questions (e), I do not know how to calculate the threshold if the P(IN=0) and P(IN=1) are different...
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Given that the probability density function of the additive channel noise is as follows N (n) 0.5 l 0 The channel response to a bit input is the sum of the response to the input and noise. Without noise, the responses to bit"" and bit "1" are 0V and 1V, respectively. Decoding the channel output is done by comparing the channel output to a threshold value of T. The decoded bit is "1" if the channel voltage is greater than T and"O" otherwise. (a) [5] Sketch the probability density function of the received signal if the input bit is "O" (b) 5] Sketch the probability density function of the received signal if the input bit is" (c) [5] What is the optimal threshold if the input bits "O" and"1" are equally likely? (d) [5] What is the bit error rate if we use the optimal threshold in 3(c)? (e) [5] Re-do parts 3(c)&(d) if the input bi "" is twice more likely to occur than the input bit"" Given that the probability density function of the additive channel noise is as follows N (n) 0.5 l 0 The channel response to a bit input is the sum of the response to the input and noise. Without noise, the responses to bit"" and bit "1" are 0V and 1V, respectively. Decoding the channel output is done by comparing the channel output to a threshold value of T. The decoded bit is "1" if the channel voltage is greater than T and"O" otherwise. (a) [5] Sketch the probability density function of the received signal if the input bit is "O" (b) 5] Sketch the probability density function of the received signal if the input bit is" (c) [5] What is the optimal threshold if the input bits "O" and"1" are equally likely? (d) [5] What is the bit error rate if we use the optimal threshold in 3(c)? (e) [5] Re-do parts 3(c)&(d) if the input bi "" is twice more likely to occur than the input bit""
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