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 an FM broadcast that employs the pre-emphasis filter with frequency response

$${H_{pe}}(\omega ) = 1 + {{j\omega } \over {{\omega _0}}}$$,

For the network shown in the figure to act as a corresponding de-emphasis filter, the appropriate pairs of (R, C) values is/are ____________.

The transition diagram of a discrete memoryless channel with three input symbols and three output symbols is shown in the figure. The transition probabilities are as marked. The parameter $$\alpha$$ lies in the interval [0.25, 1]. The value of .. for which the capacity of this channel is maximized, is __________ (rounded off to two decimal places).

Consider communication over a memoryless binary symmetric channel using a (7, 4) Hamming code. Each transmitted bit is received correctly with probability (1 $$-$$ $$\in$$), and flipped with probability $$\in$$. For each codeword transmission, the receiver performs minimum Hamming distance decoding, and correctly decodes the message bits if and only if the channel introduces at most one bit error. For $$\in$$ = 0.1, the probability that a transmitted codeword is decoded correctly is __________ (rounded off to two decimal places).