Worked out example of Slepian-Wolf Theorem
Here's a simpler example. Consider the binary erasure channel which erases its input with probability $1/2$. The channel capacity is $1/2$, so you should be able to send one bit of information by sending two bits on the channel. Or should you?

Shannon's theorem only guarantees that for every $\epsilon &gt; 0$, you can send $(1/2-\epsilon) N$ bits of information by sending $N$ bits across the channel, with failure probability approaching zero as $N\to\infty$. There are two features of this theorem (shared by Slepian–Wolf) that you didn't take into account:


The theorem talks about asymptotic rates.
The theorem allows for some small failure probability.


The article you link to assumes you are already aware of all this. Since you appear not to be, I suggest reading a textbook on information theory, where all the relevant concepts are defined and explained.