Spiking Neural Belief Propagation Decoder for LDPC Codes with Small Variable Node Degrees

Spiking neural networks (SNNs) promise energyefficient data processing by imitating the event-based behavior of biological neurons. In previous work, we introduced the enlarge-likelihood-each-notable-amplitude spiking-neural-network (ELENA-SNN) decoder, a novel decoding algorithm for low-density parity-check (LDPC) codes. The decoder integrates SNNs into belief propagation (BP) decoding by approximating the check node (CN) update equation using SNNs. However, when decoding LDPC codes with a small variable node (VN) degree, the approximation gets too rough, and the ELENASNN decoder does not yield good results. This paper introduces the multi-level ELENA-SNN (ML-ELENA-SNN) decoder, which is an extension of the ELENA-SNN decoder. Instead of a single SNN approximating the CN update, multiple SNNs are applied in parallel, resulting in a higher resolution and higher dynamic range of the exchanged messages. We show that the ML-ELENASNN decoder performs similarly to the ubiquitous normalized min-sum decoder for the $(38400,30720)$ regular LDPC code with a VN degree of $d_{v}=3$ and a CN degree of $d_{\mathrm{c}}=15$.