By binary cardinal tree, I mean a tree with degree 2.
The questions confuses my becaused I know LOUDS/DFUDS can encode binary tree with 2n bits, however this paper cliams that it is possible to encode with only n bits.
The paper was published on PODS 2008, and it provides solid inferences around the confusing point.
Thus I believe I could have missed some more succinct approach.
Related context is at Section 3, bottom right at Page 3, of the aforementioned paper.
I really appreciate any advice or suggestions.