Optimum message mapping LDPC decoders derived from the sum-product algorithm
Starting from a discrete density evolution scheme originally introduced by Brian M. Kurkoski et al. which we improved by applying the Information Bottleneck method, we recently presented results on message passing decoders for Low Density Parity Check codes that have much lower complexity than state of the art decoders. In the decoders all node operations are replaced by discrete message mappings of unsigned integers what yields a great complexity reduction. Anyway the decoders perform very close to belief propagation decoding. New included simulation results prove that using a 4 bit integer architecture these decoders loose only 0.1 dB over Eb/No in comparison to an exact belief propagation decoder applied to the quantized output of a Gaussian channel. The most important contribution of this paper is the derivation of the message mapping decoders from the sum-product algorithm. Until now these decoders are assumed to not be linked to this algorithm. In order to reveal the hidden connection, we explain the decoding principle of the message mapping decoders in general factor graphs.