|Just settled in for a long winter's nap.|
There's probably nothing better for your raised bed than shredded leaves left to rot on top of it over the winter. In fact, I won't even bother to fertilize any of the beds that I so treat - no compost, certainly no chemicals - even though I plan to plant heavy-feeding sweet corn in this bed next year. A few inches of leaves rotted into the soil provide everything you'll need, even after doing the yeoman's work of smothering everything that tries to sprout from that bed in the next 5 months. It is, IMO, the best thing you can do for a raised bed. You just have to have enough leaves.**
That said, you'll notice that there are three 2'x2' beds behind this 4'x8' one, and they don't look like they've received the same courtesy. That's because they haven't, and may not at all this winter. The bed on the top left has no cover at all. It's got spinach growing in it, and obviously will not flourish if I pile a bunch of shredded leaves on it. The one on the right has shredded paper that is nearly rotted in. There's no sense in removing that. But the one in the center has a brand new crop of shredded paper just added, and the reason for that is that it's got a bunch of 6" garlic plants growing out of it.
Shredded paper is not nearly as good for your soil as leaves. While keeping the soil protected like leaves do, it really provides no nutrients. Your soil needs far more added than this sterile cap can provide.
But there's one thing it's great for: keeping its form. When I have 15 little garlic shoots growing, I can pack around them with wet, shredded paper and be certain that the paper, once dried, will hold that exact form until I rip it out. Rain doesn't faze it, wind doesn't move it. The garlic will die back over winter, but when it pops out in the spring there will be a little hole in the bed's cap in exactly the right place. Leaves will give you no such courtesy.
Once I pull the garlic, about July 1, I'll add a couple inches of compost before I plant again, probably from these very leaves. After all, in addition to my new 600 pounds of leaves, I have all the leaves that I would normally rake and rot. And the ladies are not terribly happy about that....
* Well, not next-door type neighbor. More like next-town-over. Hi, Dorothy and Marvin. Love you guys.
** Obviously, the more beds you have, the harder it becomes to give them all the treatment. Thus my casting about for other people's yard waste. Preferably delivered.