Let H(X) denote the entropy of a discrete random variable X taking K possible distinct real values. Which of the following statements is/are necessarily true?
A symbol stream contains alternate QPSK and 16-QAM symbols. If symbols from this stream are transmitted at the rate of 1 mega-symbols per second, the raw (uncoded) data rate is _________ mega-bits per second (rounded off to one decimal place).
Consider a channel over which either symbol xA or symbol xB is transmitted. Let the output of the channel Y be the input to a maximum likelihood (ML) detector at the receiver. The conditional probability density functions for y given xA and xB are :
$${f_{\left. Y \right|{x_A}}}(y) = {e^{ - (y + 1)}}u(y + 1)$$,
$${f_{\left. Y \right|{x_B}}}(y) = {e^{(y - 1)}}(1 - u(y - 1))$$,
where, u( . ) is the standard unit step function. The probability of symbol error for this system is _________ (rounded off to two decimal places).
