  In this paper we consider the lossy compression of a binary symmetric source.
We present a scheme that provides a low complexity lossy compressor with near
optimal empirical performance. The proposed scheme is based on b-reduced
ultra-sparse LDPC codes over GF(q). Encoding is performed by the Reinforced
Belief Propagation algorithm, a variant of Belief Propagation. The
computational complexity at the encoder is O(<d>.n.q.log q), where <d> is the
average degree of the check nodes. For our code ensemble, decoding can be
performed iteratively following the inverse steps of the leaf removal
algorithm. For a sparse parity-check matrix the number of needed operations is
O(n).
