PYQs Based Test - 11 : Communications

A linear Hamming code is used to map 4-bit messages to 7-bit code words. The encoder mapping is linear. If the message 0001 is mapped to the code word 0000111, and the message 0011 is mapped to the code word 1100110, then the message 0010 is mapped to

An analog baseband signal, band-limited to 100 Hz, is sampled at the Nyquist rate. The samples are quantized into four message symbols that occur independently with probabilities p₁ = p₄ = 0.125 and p₂ = p₃. The information rate (bits/sec) of the message source is __________

A binary source generates symbols 𝑋 ∈ {−1, 1} which are transmitted over a noisy channel. The probability of transmitting 𝑋 = 1 is 0.5. Input to the threshold detector is 𝑅 = 𝑋 + 𝑁. The probability density function *f${}_N$ *(𝑛) of the noise 𝑁 is shown below:



If the detection threshold is zero, then the probability of error (correct to two decimal places) is ________.

Which one of the following statements about differential pulse code modulation (DPCM) is true?

A speech signal, band-limited to 4 kHz, is sampled at 1.25 times the Nyquist rate. The speech samples assumed to be statistically independent and uniformly distributed in the range -5 V to +5 V, are subsequently quantized in an 8-bit uniform quantizer and then transmitted over a voice-grade AWGN telephone channel. If the ratio of the transmitted signal power to channel noise power is 26 dB, the minimum channel bandwidth required to ensure reliable transmission of the signal with an arbitrarily small probability of transmission error (rounded off to two decimal places) is _______ kHz.