is it possible for me to publish work that is based on someone else's patented tech?

A patent provides the owner of the patent with the exclusive right to prevent any other party, not authorized by the patent owner, to make, sell, or use the patented technology. I assume from your post that you are not actually making, using, or selling the patented product, device, whatever, but just writing about it. Patents per se are public documents, so you are free to use any written material contained in the patent. You may also improve the patented device but beware that if, for example, you physically embody the improvement, you may be infringing the patent even though you yourself may be entitled to a patent upon the improvement. Here is a very basic situation - let's say that you are the first one to invent a chair - so you claim and patent a chair comprising at least one leg (could be a pedestal-type chair), a seat, and a back. Someone comes along and wants to improve the chair by adding a seat cushion, or arms to the chair, for more comfort. They then receive their patent. However, they cannot make, use, or sell their own chair because they would be infringing your patent.
On the other hand, you become aware of their improved chair and you want to make, use, or sell the improved chair because it is in fact more comfortable, but you cannot make, use, or sell the improved chair because you will infringe that patent. What to do? You both cross-license each other permitting each to manufacture the improved chair without infringing each other's patents.