# 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? – Marcus Müller 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. – Dilip Sarwate 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! – CristoJV 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! – CristoJV Oct 6 '17 at 6:58