Information-Optimum LDPC Decoders Based on the Information Bottleneck Method

The Information Bottleneck method is a powerful and generic tool from the field of machine learning. It compresses an observation to a quantized variable while attempting to preserve the mutual information shared with a relevant random variable. This paper describes a new application of the Information Bottleneck method in communications. It explains in detail, how the Information Bottleneck method can be applied to construct discrete message passing decoders for regular low-density parity-check codes. The obtained decoders process only unsigned integers and use only simple lookup tables as node operations. As a consequence, the decoders can be implemented using only unsigned integer arithmetic which makes them significantly simpler and faster than the state-of-the-art decoders which process real valued log-likelihood ratios. Anyway, included results show that the considered discrete message passing decoders perform surprisingly close to optimum message passing decoders and even outperform state-of-the-art decoders, such as the min-sum decoder. We aim to take the reader on a journey from the theoretical idea of the Information Bottleneck method to a complete design framework for the considered discrete decoders. Several included figures and examples illustrate the decoder construction process and its analysis.