21. What is the channel capacity of a noisy channel with conditional probability of error p = $$\frac{1}{2}$$?
22. A binary symmetric channel with p as transition probability, uses repetition code 'n' times, with n = 2m + 1 being an odd integer. In a block of n bits, if the number of zeros exceed number of ones, decoder decodes it as "0" otherwise as "1". An error occurs when m + 1 or more transmission out of 3 are incorrect, what is the probability of error?
23. Over a certain binary communication channel, the symbol 0 is transmitted with probability 0.4 and 1 is transmitted with probability 0.6. It is given that p(ε/0) = 10-6 and p(ε/1) = 10-4, where p(ε/xi) is the probability of detecting the error given that xi is transmitted. What is the error probability of the channel?
24. Entropy of a source with 4 symbols is maximum possible. What would be the average Huffman code length of this source?
25. . . . . . . . . is the average amount of information that must be delivered in order to resolve the uncertainty about the outcome of a trial.
26. A prefix code is . . . . . . . . decodable and satisfies . . . . . . . . inequality.
27. The minimum transmitter power requirement in the absence of channel coding of a communication system is 2 W. If a channel coding scheme of 3 dB is incorporated in the system, the minimum required transmitter power is
28. A communication system is used to transmit one of 16 possible signals. Assume that transmission is accomplished by encoding the signals into binary digits. Further assume that signals are equally likely to occur. If each binary digit requires 1µ sec. For transmission, then how much information (in bits) is transmitted by the system in 8 microseconds?
29. The average information associated with an extremely unlikely message is zero. What is the average information associated with an extremely likely message?
30. A telephone channel has bandwidth B of 3kHz and SNR (S/ηB) of 30 dB. It is connected to a teletype machine having 32 different symbols. The symbol rate required for errorless transmission is nearly
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