# Data rate with modulation and conventional encoding

I had a rather simple question. Say I had a SISO communications system with an information data rate of 50 Mbps that uses QPSK modulation and a rate 1/2 conventional coding. What would be my symbol rate?

I assumed that it would follow something like: $$Rs = \frac{(50 \times 10^{6})}{(1/2)} = 100Mbps \div 2 = 50 Msym/s$$

Looking at this, my logic doesn't seem quite right. Would a conventional code cancel out a QPSK modulation scheme? I understand that QPSK would use 2 bits per symbol, but as I also understand it, a rate 1/2 encoder would have twice as many bits in the output?

Thanks for your time, and help in advanced - I really appreciate it!