  We construct an infinite family of bounded-degree bipartite unique-neighbour
expander graphs with arbitrarily unbalanced sides. Although weaker than the
lossless expanders constructed by Capalbo et al., our construction is simpler
and may be closer to be implementable in practice due to the smaller constants.
We construct these graphs by composing bipartite Ramanujan graphs with a
fixed-size gadget in a way that generalizes the construction of unique
neighbour expanders by Alon and Capalbo. For the analysis of our construction
we prove a strong upper bound on average degrees in small induced subgraphs of
bipartite Ramanujan graphs. Our bound generalizes Kahale's average degree bound
to bipartite Ramanujan graphs, and may be of independent interest.
Surprisingly, our bound strongly relies on the exact Ramanujan-ness of the
graph and is not known to hold for nearly-Ramanujan graphs.
