  The Ascending Subgraph Decomposition (ASD) Conjecture asserts that every
graph $G$ with ${n+1\choose 2}$ edges admits an edge decomposition
$G=H_1\oplus\cdots \oplus H_n$ such that $H_i$ has $i$ edges and it is
isomorphic to a subgraph of $H_{i+1}$, $i=1,\ldots ,n-1$. We show that every
bipartite graph $G$ with ${n+1\choose 2}$ edges such that the degree sequence
$d_1,\ldots ,d_k$ of one of the stable sets satisfies $ d_{k-i}\ge n-i\;
\text{for each}\; 0\le i\le k-1,$, admits an ascending subgraph decomposition
with star forests. We also give a necessary condition on the degree sequence
which is not far from the above sufficient one.
