Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
Improved low-density parity-check codes using irregular graphs
IEEE Transactions on Information Theory
The capacity of low-density parity-check codes under message-passing decoding
IEEE Transactions on Information Theory
A coding theorem for lossy data compression by LDPC codes
IEEE Transactions on Information Theory
Design and analysis of nonbinary LDPC codes for arbitrary discrete-memoryless channels
IEEE Transactions on Information Theory
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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 ultrasparse 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.log2 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).