Step 1: Group organisms by how they feed.
In an ecosystem some organisms make their own food, some eat others, and some feed on dead remains.
Step 2: Identify the food makers.
Autotrophs, such as green plants, build their own food, so they are not the answer.
Step 3: Identify the consumers.
Heterotrophs eat ready-made food from other organisms, so they do not break down dead matter on their own.
Step 4: Set aside the aerophyte.
An aerophyte is a plant that grows in air, not a decomposer.
Step 5: Find the decomposers.
Saprotrophs feed on dead and decaying organic matter, breaking complex compounds down into simpler ones.
Step 6: Conclusion.
The biotic community that breaks down complex organic compounds in dead matter is the saprotrophs.
\[ \boxed{\text{Saprotrophs}} \]