Trellis based node operations for LDPC decoders from the Information Bottleneck method

We utilize the Information Bottleneck method in a discrete density evolution scheme that was introduced by Brian M. Kurkoski et al. in order to find message mappings for the node operations of discrete LDPC decoders. The resulting decoders have performance close to belief propagation decoding but require much lower implementation efforts because they only process unsigned integers instead of log-likelihood-ratios. An efficient trellis implementation of the resulting discrete node operations is presented. In the trellis implementation the passed messages are calculated using recursive formulas that are fully characterized by two static vectors of integers. Bit error rate simulations for exemplary (3, 6)-regular LDPC codes with a 4 bit message representation prove the performance of the proposed decoders that even outperform Min-Sum decoders with quasi continuous message representation.