What are Nyquist and Shannon criteria in digital communications, and how do they relate to channel capacity and BER?

• A. Nyquist rate defines sampling frequency for minimal distortion; Shannon limit defines maximum information rate given bandwidth and SNR; they relate to achievable BER and data rate
• B. Nyquist defines thermal noise limit; Shannon defines quantization levels
• C. Nyquist sets modulation order; Shannon defines code rate
• D. Nyquist and Shannon are unrelated to BER

Answer: (A)

The main idea tested is how two fundamental limits shape digital communications. Nyquist criteria tell you how fast you can modulate and sample signals over a given bandwidth without distortion or intersymbol interference. In a bandwidth-limited channel, the practical rule is that you can support roughly 2B symbols per second (with proper pulse shaping) without smearing them together, and this guides how you design signaling and sampling to preserve the information you send.

Shannon’s capacity bound then tells you the ultimate ceiling on how many bits per second you can reliably convey over that same channel, given its bandwidth and noise level. The capacity is C = B log2(1 + SNR) for an AWGN channel, which sets the maximum data rate at which error-free communication is theoretically possible with optimal coding. BER, or bit error rate, depends on the actual operating point: with a rate below this capacity and good coding, you can achieve very low BER even in the presence of noise; if you push the rate toward or beyond the capacity, reliable communication becomes impossible and BER stays high.

So the correct idea links Nyquist to how fast you can signal without distortion for a given bandwidth, and Shannon to the ultimate reliable data rate given bandwidth and noise, with BER governed by the SNR, the chosen rate, and the effectiveness of coding.