  A quantized message passing decoding algorithm for low-density parity-check
codes is presented. The algorithm relies on the min approximation at the check
nodes, and on modelling the variable node inbound messages as observations of
an extrinsic discrete memoryless channel. The performance of the algorithm is
analyzed and compared to quantized min-sum decoding by means of density
evolution, and almost closes the gap with the performance of the sum-product
algorithm. A stability analysis is derived, which highlights the role played by
degree-$3$ variable nodes in the stability condition. Finite-length simulation
results confirm large gains predicted by the asymptotic analysis.
