Relationship between $E_b/N_0$ and $\rm SNR$ with channel coding I would like to know what would be the relationship between $E_b/N_0$ and $\rm SNR$ when there is a coding rate of $R_c=K/N$. Normally when there is no channel coding according to this link.

$$\textrm{SNR(dB)} = \frac{E_b}{N_0}(\textrm{dB}) + 10\log10\left(\frac{R_b}{B}\right)$$

However what would happen if I have a linear block code or other coding schemes with code rate $R_c =1/2$ or other values, how to calculate the relationship between $\rm SNR$ and $E_b/N_0$ in this case ?
The relationship between SNR and $E_b/N_0$ is independent of the code rate. Note that $E_b$ is the energy per data bit (not the coded bits), and $R_b$ is the (uncoded) data bit rate. As long as you keep using these values, you can use the formula given in your question. Of course, when going from an uncoded system to a coded system, the values of $E_b$ and $R_b$ will usually change, so the resulting SNR will generally be different.