Commentary for Sukkah 1:3
פֵּרַס עָלֶיהָ סָדִין מִפְּנֵי הַחַמָּה, אוֹ תַּחְתֶּיהָ מִפְּנֵי הַנְּשָׁר, אוֹ שֶׁפֵּרַס עַל גַּבֵּי הַקִּינוֹף, פְּסוּלָה. אֲבָל פּוֹרֵס הוּא עַל גַּבֵּי נַקְלִיטֵי הַמִּטָּה:
If he spread a sheet over it because of the sun, or under it (i.e., under the schach) because of the fall, or on the kinof, it is pasul. [("the fall":) so that leaves and twigs not fall upon the table. Another interpretation: so that the leaves not fall when they dry up and the succah remain "its sun greater than its shade." A sheet can acquire tumah (uncleanliness) and is (therefore) pasul as schach. And this is so only (if he spreads the sheet) because of the fall; but if he does so to beautify (the succah) it is kasher. ("or on the kinof":) That is, even if he did not spread it because of the fall, but for decoration, on his bed, on the kinof — four poles for the four feet of his bed, which are high. He places poles from one to the other on top of them at a distance from the schach, so that now he is not using something that acquires tumah as schach, for he did not place it there for that purpose. It is pasul, for (in such an instance) he is not dwelling in a succah, a tent intervening.] But he may spread it on the naklitin (the posts) of the bed, [which are only two, in the middle of the bed, one at the head, the other at the foot. A pole is extended from one to the other and a sheet paced on it. And because it does not have a roof a handbreadth wide, it is not called a tent.]
Bartenura on Mishnah Sukkah
English Explanation of Mishnah Sukkah
Or if he spread [a sheet] over the frame of a four-post bed, [the sukkah] is invalid.
But he may spread it over the frame of a two-post bed.
This mishnah teaches that if there is a roof-like structure underneath or above the sukkah it invalidates the skhakh.
Section one: If he spread a sheet on top of the sukkah to keep out the sun, or a sheet underneath the skhakh to keep out the falling leaves, the sheet invalidates the sukkah. This is because a sheet cannot be used for skhakh, so in essence he is using invalid skhakh to form his sukkah.
Section two: Similarly, if he spreads a sheet over a four-post bed, the sheet invalidates his skhakh, because the sheet forms a roof. However, the sheet does not invalidate the skhakh if it was spread over a two-post bed. This is because the sheet forms a tent-like structure, one that slopes to the sides and is not considered a roof. Since there is no roof made of a sheet, the only roof is the skhakh and the sukkah is valid.