First, the host of the world building a room with a carpet. The ceiling is right on you head (2 blocks high) and make no walls. The image is what you have to make. Try to fit in it, and you can't.
EDIT: but you can fit under the block if you dig a hole beside the carpet and use autojump...
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Confirmed to affect 0.12.3 on iPhone 6+ (iOS 9.1). Jumping while walking forward against the space will allow the player to enter.
You can get through the 2 high gap with carpet if you jump, not by just walking through. 0.14.3 Win 10
Comfirm on iPad 4 too!