What is the relationship between Noise variance and Binary Rate?

I have one channel with its maximum capacity $C_s$ defined by SNR [30dB] using the Shannon Theorem.

Using that information I can get the top limit of my binary transmission rate. $R\le C_s$.

I want to transmit a gray leveled television signal with 4,5MHz bandwidth (only pixel information). So I can feed 576*720*25Hz pixels per second with 20 gray levels, at the limit of $C_s$.

The question is, how can I get the noise variance if I increase the binary Rate (using for example 25 levels) greater than $C_s$. I can imagine that if I increase $R$, noise variance is increased, but how can I simulated using a matlab program.

The noise is consider gaussian additive noise with median zero, and variance $\sigma^2$. The image is equally distributed around all pixel levels.

• The noise variance has nothing to do with the rate you're using. So, to me, your question makes no sense - why would the noise variance change if you changed rate? Sep 29 '17 at 17:44
• Which Shannon Theorem are you talking about? One of them has nothing to do with noise variance, and the other doesn't mention anything about levels of any kind. Sep 29 '17 at 19:40
• Guys @MarcusMüller. Thank you for your answers, you are right I had a mess in my brains that question doesn't make any sense, thanks to you know I solve correctly my problem. Thank you! Oct 6 '17 at 6:57
• Guys @DilipSarwate Thank you for your answers, you are right I had a mess in my brains that question doesn't make any sense, thanks to you know I solve correctly my problem. Thank you! Oct 6 '17 at 6:58