  The encoder and decoder for lossy data compression of binary memoryless
sources are developed on the basis of a specific-type nonmonotonic perceptron.
Statistical mechanical analysis indicates that the potential ability of the
perceptron-based code saturates the theoretically achievable limit in most
cases although exactly performing the compression is computationally difficult.
To resolve this difficulty, we provide a computationally tractable
approximation algorithm using belief propagation (BP), which is a current
standard algorithm of probabilistic inference. Introducing several
approximations and heuristics, the BP-based algorithm exhibits performance that
is close to the achievable limit in a practical time scale in optimal cases.
