Leader–Tan edge-decomposition conjecture for hypercubes

Let $H$ be a non-empty subgraph of the hypercube $Q_k$ for some $k$. Leader–Tan edge-decomposition conjecture. There exists a positive integer $n$ such that the edges of $Q_n$ can be covered by edge-disjoint copies of $H$; the copies of $H$ are not required to be induced. This is the edge-decomposition analogue of partitioning hypercube vertices into fixed subgraphs. The source states that the conjecture is difficult even for $H$ equal to $Q_k$ with one edge removed, while some path cases are known.