How to deal with papers/authors that provide no details of implementation? I was reading a conference paper relevant to my area of study, and I found it interesting - they did what I was planning to do anyways, and had some extremely promising results.

Now, I don't really believe their claims, as the success seems a bit extreme (300-400x speed up for an algorithm by switching from CPU to GPU). It feels like they compared optimized GPU code to an unoptimized CPU algorithm. Nevertheless, I am in general a reasonable person, so I wanted to see what they did and how they did it.

Unfortunately, the paper is very vague on the implementation used. There is a snippet of pseudocode that doesn't really share anything new (it is obvious). I emailed the authors and asked them for source code, if at all possible. The first author replied to me, and provided a GitHub link. The code in the repository is undocumented, and isn't exactly for the implementation I asked about anyways. It is for another implementation they did (also distributed computing).

I tried contacting the author with some questions, but he has never responded to me again... So that link has not been successful.

The paper doesn't have many citations, and all of them but one are self-references. I haven't found evidence that anyone built on these findings so far.

So: I figured I would just move ahead with my idea and not rely on their implementation. However, do I need to address this paper somehow in my thesis? I assume so - the committee could ask me about it, and how my work is different. But how can I compare my work to something else that I have no source code for? Do I take their word for it and compare my results to their published results? Am I allowed to criticize work that provides no supporting code? Probably not...

Should I pester the authors some more? They are probably sick of me by now.
In your thesis, I think it should be safe to say something along the lines of 


  "John Doe et. al. claim in [22] that the algorithm would run 400X faster with their implementation, however, the details are unclear."


and leave it there. If you are asked more about it in your defense, you may politely state that you tried to approach the authors for more information but could not get it.