How to train the discriminator part of InfoGAN

Question

I am new to GAN, and is currently studying different types of GANs, and InfoGAN is one of them. I am a little confused with the way to train a InfoGAN discriminator model. Like vanilla GAN, when training discriminators, real and fake samples are fed to the discriminator for parametric updating.

Here is the problem confusing me:

Since there is an auxiliary classifier to classify the sample, is it correct to label (give each real sample a domain code) the real samples first when I train this part?

Thanks in advance.