GATE EC 2012 Set 1 Q3 — Digital Communications

Consider a discrete memoryless source with an alphabet of four source symbols. $s(t)$ is a multi-level $(-1,0,+1,+2)$ signal representing a long sequence of random symbols from the above source which is generating $10^{4}$ symbols per second. Which of the following options is the correct value of equivalent Nyquist bandwidth of $s(t)$?

A wireless digital transmission scheme is using $16$-QAM over an additive white Gaussian noise channel and a maximum-likelihood receiver. Consider the information bit rate from source to be $4 \times 10^{6}$ bits per second. The minimum transmission bandwidth (in MHz) of the modulated signal necessary for optimum recovery of information at the receiver …

A QPSK modulated signal from an additive white Gaussian noise (AWGN) channel is received with an $E_{b} / N_{o}=8.4 \mathrm{~dB}$ at the input of a coherent QPSK demodulator. A maximum-likelihood reception method is used in the demodulator. Assume the complimentary error function …

The average bit error rate at the input of a $(7,4,1)$ Hamming decoder is $0.10$. The probability that the decoder will fail to decode a received word correctly is $\_\_\_\_\_$ (rounded off to two decimal places)

The generator matrix of a $(6,3)$ binary linear block code is given by $$G=\left[\begin{array}{llllll} 1 & 0 & 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & 1 & 1 & 0 \end{array}\right]$$ The minimum Hamming distance $d_{\text{min }}$ between codewords equals _________ (answer in …

A digital communication system transmits through a noiseless bandlimited channel $[-W W]$. The received signal $z(t)$ at the output of the receiving filter is given by $z(t)=\sum_{n} b[n] x(t-n T)$ where $b[n]$ are the symbols and $x(t)$ is the overall system response to a single symbol. The received signal is sampled at $t=m T$. The Fourier …