A lossy data compression scheme for uniformly biased Boolean messages is investigated via statistical
mechanics techniques. We utilize a treelike committee machine committee tree and a treelike parity machine
parity tree whose transfer functions are nonmonotonic. The scheme performance at the infinite code length
limit is analyzed using the replica method. Both committee and parity treelike networks are shown to saturate
the Shannon bound. The Almeida-Thouless stability of the replica symmetric solution is analyzed, and the
tuning of the nonmonotonic transfer function is also discussed.