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

TL;DR

This work addresses LDPC decoding with small variable-node degrees by replacing CN updates with multi-SNN blocks, enabling higher message resolution and dynamic range. The proposed ML-ELENA-SNN extends ELENA-SNN with $L$ parallel SCNUs per CN, each possessing distinct thresholds, allowing the CN messages to accumulate over multiple levels. Results show near-normalized min-sum performance for a $(38400,30720)$ code with $d_v=3$, and competitive performance for a $(273,191)$ code with larger $d_v$, illustrating a favorable complexity-accuracy trade-off for small-$d_v$ LDPC codes. The approach supports energy-efficient, neuromorphic-like decoding while highlighting the need to balance $L$ and hardware costs across code parameters.

Abstract

Spiking neural networks (SNNs) promise energy-efficient 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 ELENA-SNN 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-ELENA-SNN decoder performs similarly to the ubiquitous normalized min-sum decoder for the (38400, 30720) regular LDPC code with a VN degree of dv = 3 and a CN degree of dc = 15.

Figures (8)

• Figure 1: Example of the dynamics of an neuron. The input spikes $s_\mathrm{in}(t)$, denoted by purple dots, induce the synaptic current $i(t)$, which charges the membrane potential $v(t)$. If $v(t)$ exceeds the threshold $v_\mathrm{th}$, an output spike $s_\mathrm{out}(t)$ is fired, and $v(t)$ is reset.
• Figure 2: SCNU that computes the message $L_{i\leftarrow j}^{[\mathrm{c}]}$ based on the incoming messages ${L^{[\mathrm{v}]}_{i'\rightarrow j},~i'\in \mathcal{M}(j)\setminus\{i\}=:\{i_1,\ldots,i_{d_\mathrm{c}-1}\}}$. The top and bottom branches approximate \ref{['eq:cn_update_alpha']} and \ref{['eq:cn_update_beta']}, respectively. The LI neuron serves as the memory element.
• Figure 3: Structure of the SNN block from Fig. \ref{['fig:SPC_SRNCTMS']}, implementing \ref{['eq:elena_offset']} using $d_\mathrm{c}$ neurons. If an input falls below $\theta_1$, the connected neuron is charged to trigger a spike. The upstream neuron aggregates all incoming spikes and forwards one, resulting in a zero output. If all inputs exceed $\theta_1$, no neurons are charged, producing $\theta_2$ as the output.
• Figure 4: Architecture of the proposed decoder. The SCNU contains the SNN. For ${i\in \{1,\ldots,N\}}$ and ${j\in \{1,\ldots,M\}}$, the notation ${\mathcal{N}(i):=\{j_1^i,\ldots, j^i_{d_v}\}}$ and $\mathcal{M}(j):=\{i_1^j,\ldots, i^j_{d_v}\}$ is used.
• Figure 5: SCNU of the proposed decoder.