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.