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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(&lt; d &gt; .n.q. log<sub>2</sub> q), where &lt; d &gt; 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).

Efficient LDPC codes over GF(q) for lossy data compression