Matched Quantized Min-Sum Decoding of Low-Density Parity-Check Codes

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.