One sided label smoothing in GANs
Well, let's start with what label smoothing is. We replace the 0s and 1s in one hot encoding for example for the MNIST dataset with 10 classes by smoothed values e.g.: 0.1 for 1, 0.9 for 9 etc. 

If we replace positive classification targets with $\alpha$ and negative targets with $\beta$ the optimal discriminator $D$ becomes: 

$$D(x)=\frac{\alpha p_{data}(x) + \beta p_{model}(x)}{p_{data}(x) + p_{model}(x)}$$.

Where the $p_{data}(x)$ corresponds to the original distribution; at least we think. And the $p_{model}(x)$ corresponds to the distribution that we want to target and $x$ are the input features to the discriminator $D$. 

Now, when $\beta \neq 0$, erroneous samples from $p_{model}$ have no incentive to move nearer to the data i.e. it reinforces current generator behaviour. Hence, we smooth only the positive labels to $\alpha$, leaving negative labels set to 0. This behaviour prevents discriminator from giving very large gradient signal to the generator.