A PhD program is principally about training you to be a researcher. Research is all about doing things no one else has done before and pushing the boundaries of knowledge.
A necessary first step is to get some understanding of what others have done before you. Unlike coursework where you typically learn things that "everybody" knows, when you do research you often need to understand what other people on the boundary of some specialized area of knowledge are doing: you have to be able to read their papers and understand what they are doing.
If you're in a field that involves algorithms and computation, one of the ways to understand what is going on is to take algorithms that other people describe and code them up in a way that you can test them and probably replicate the results of the paper. This is also a first step to either modifying their work or to making a comparison to something else you might design.
The thing you are meant to be learning is not only how some algorithm works or should be implemented, but also in learning how to learn. You won't learn how to learn if you rely on someone else teaching you all the time. So, yes, it's normal to be expected to do these things on your own (for the most part). It's not a job where the goal is actually to replicate these papers in the most efficient way with the personnel available, the goal is your own learning how to understand and do things.
That said, it's okay to get stuck and ask for help. It's just that you should make a lot of your own effort first.