Modulation and coding selection¶

As developed in "Constraints for the physical layer" , we have the following relation between the modulation, the coding and the roll-off:

$\frac{\log_{2}(M)\rho}{1+\alpha}>\frac{R_{b}}{B}$

For the sake of simplicity, we will fix the roll off to $\alpha=0.2$, which is a typical value enabling a good tradeoff between the spectral efficiency and the threshold detector performances (used in DVB-S2 for example).

Then, considering that M is a power of 2 and $\rho<1$, we can estimate from the previous relation the minimal MODCOD required:

$M = 2^{nextpow2(2^{\frac{(1+\alpha)*R_{b}}{B}})}$

$\rho = \frac{(1+\alpha)\cdot R_{b}}{B\cdot log_{2}(M)}$

Conclusion: After fixing the value of the roll-off (here $\alpha=0.2$), the MODCOD is directly conditioned by the values of B and Rb.