Succah Daf Yud amud beis
According to the first tosafos in the second perek of succah (first half), the reason shmuel holds that a there must be 10 teffachim under a bed is because it is the same type of din as succah al gabei succah which also needs 10 teffachim in order to pasul. If this is so, why then under a "kinofos (4 post bed)" just because it is kevah its pasul, shouldn't it also need 10 teffachim to fall into the category of succah al gabei succah? Why should the fact that its kevah make any difference?
Also, why don't we find a halacha that " no"iee succah (decorations) that are separated by four teffachim from the schach " also have to be 10 teffachim from the ground in order to be considered an ohel ( or succah al gabei succah) ???
Your question is basically the Gemara's question (10b); after the Gemara says that Kenafos are Kavu'a, the Gemara asks what is the difference betwen Kenafos and Sukah Al Gabei ha'Sukah. In whatever way we are to understand the Gemara's answer (b'Pashtus, it is a d'Rabanan, as Tosfos writes), the Gemara says clearly that Naklitin are comparable to Sukah Al Gabei ha'Sukah, while Kelunsos are not. Tosfos is merely following the Gemara.
The logic of Keva is that it has a Chashivus of an Ohel, since the person is finding shelter there, rather than in the upper Ohel.
As for Noy Sukah, obviously Sukah Al Gabei ha'Sukah does not apply, for it is Sechach Pasul. We would also then need ten from the Noy to the Sechach. As far as having ten underneath it, since it is a whole Mechitzah it is Mevatel the upper Sechach even without having ten, for it is now the thing which is Ma'ahil on the person. In the case of a bed, we may still say that he is under the Ohel of the Sechach if the bed does not have a Chashivus.
D. Zupnik
In the case of Kri'as Shema, the Ritva explains that the area less than ten is considered a "Malbush" -- "article of clothing" not an Ohel. This is as opposed to Shabbos and Tum'ah where there is no person involved to ensure the covering is not an Ohel. [Another answer can be derived from the explanation of the Sfas Emes on our Gemara, see at length].
Kol Tuv,
Yaakov Montrose