Someone sent me the image below, and I think I'm confused as well.
Is the second formula (modulation) correct? What does it mean? From the symbol, I think it represents capacity, but it doesn't make much sense to me.

1. Shannon capacity: $ C = B \log_{2}(1+\text{SNR}) \text{ bps} $

2. Modulation: $ C = B \log_{2}(M) \log_{2}(1+\text{SNR}) $

enter image description here


1 Answer 1


since $(2) > (1)\quad\forall M>2$, and $(1)$ is an upper bound, $(2)$ must be incorrect, assuming it describes the same $C$.

  • $\begingroup$ Thanks. Can you guess what they could possibly mean by (2)? $\endgroup$
    – internet
    Commented May 1 at 18:45
  • $\begingroup$ no, not really. And it's not that sensible to try and interpret screenshots of blackboards without the accompanying lecture, so I'd really think it's better if I don't speculate there :) $\endgroup$ Commented May 1 at 20:27

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