# Is there any formula for coding gain of Turbo code?

I want to compare throughput under different MCS( modulation and coding scheme).

We know Shannon capacity $C = B \log(1+SNR)$ can be used to calculate throughput by SNR. However, there is no MCS parameter in this formula.

I want to calculate throughput using following formula:

$${\rm throughput} = B \cdot ( {\rm code rate} ) \cdot \log(M) \cdot (1-P(r \cdot G(r))).$$

where $B$ is bandwidth, $M$ is constellation size, $P()$ is bit error rate function, $G()$ is coding gain function, $r$ is SNR,

For example, 64QAM code rate 0.5 throughput will be $B \cdot 0.5 \cdot 6 \cdot (1-P(r \cdot G(r)))$. However, it seems that no mathematical formula to calculate coding gain for turbo code.

I want to find a rough coding gain formula to compare different MCS performance.

Is there any formula for coding gain of Turbo code?

Or if there exist general formula to map MCS to bit error rate without considering which code is use?

any idea/reference will be great help on this regard. Thanks.

• Do you have a particular turbo code in mind? They will have very different properties based on the specific codes used in them. – Jason R Feb 23 '16 at 3:16