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I am trying to solve the below problem and I was not able to find the relation between bandwidth, Nyquist criteria and quantization. Can you please provide some hint?

Imagine that the possible transmissible symbols are 64. Whenever the transmitter needs to transmit a value=n, it sends n-1 bits to the channel, each one T/(n-1) seconds apart starting from the beginning of the same slot. What is the maximum bandwidth of an analog signal that can be transmitted without losing any information through this system if 4 bits are used for its quantization?

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  • \$\begingroup\$ Saying "Nyquist Criteria" is vague. What do you mean by Nyquist Criteria? I'll give you some examples: Nyquist Stability Criterion, Nyquist Sampling, Nyquist ISI Criterion, Nyquist Frequency... etc. \$\endgroup\$ – KingDuken Mar 14 '18 at 3:37
  • \$\begingroup\$ Thanks @KingDuken for the quick comment to clarify the question. I am referring to Nyquist Criteria that states that a channel with bandwidth B Hz can be used to carry atmost 2B signal changes (symbols) per second. \$\endgroup\$ – The Voyager Mar 14 '18 at 3:38
  • \$\begingroup\$ Okay, that's Nyquist Frequency :) \$\endgroup\$ – KingDuken Mar 14 '18 at 3:40
  • \$\begingroup\$ Thanks @KingDuken for the clarification. can you please let me know if there is any formula that relates bandwidth and quantization? \$\endgroup\$ – The Voyager Mar 14 '18 at 3:43
  • \$\begingroup\$ With 4 bits quantization, what is your value for the SNR? And is that SNR a proper/meaningful number to use in the Nyquist equation for transmittable information per second? \$\endgroup\$ – analogsystemsrf Mar 14 '18 at 3:50
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Shannon-Hartley Theorom proved the maximum Channel capacity,C and Channel Bandwidth, B.

C/B=Log_2(1+S/N)=C/B

for BER of 1e-6 results in Ref indicate ;

BPSK needs 11 dB SNR @ C/B=1
64-QAM needs 27 dB SNR @ C/B=6.33
1024-QAM needs 39 dB SNR @ C/B=8 excluding 20% overhead for FEC.

Ref

https://www.csie.ntu.edu.tw/~hsinmu/courses/_media/wn_11fall/rate_adaptation.pdf
http://www.scte.org/TechnicalColumns/12-10-01%20spectral%20effieciency.pdf
https://www.embedded.com/print/4017668
http://www2.ensc.sfu.ca/people/faculty/cavers/ENSC805/classnotes/c4p3.pdf

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Any time a signal is transmitted through a system, INFORMATION will be lost.

Because noise will be added, and the SNR will be degraded, and INFORMATION will be lost.

To lose no information in your 64-symbol system, there can NEVER be any bit errors. But random noise will at some time add up to cause bit errors.

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