"Greed" is defined as "excessive or rapacious desire, especially for wealth or possessions." Personally, I would define it as "wanting more than one deserves or is entitled to."
The trouble with this: who defines what is "excessive," or what a person "deserves" or "is entitled to?" Under professedly Communist regimes, that has always wound up being the government.
In reality, "greed" is simply the flip side of envy: a person who is "greedy" is someone who has a lot more stuff than I do, which is perceived as unfair. It is not an objective standard by any means.
Communism is fundamentally flawed not because people are "greedy," but because they naturally act in their own self interest,