Improved Generalized Automorphism Belief Propagation Decoding

TL;DR

The paper tackles the short-blocklength LDPC decoding gap between belief propagation and maximum-likelihood decoding by enhancing automorphism-based ensemble decoding. It introduces iGAED, which merges the preprocessing step of generalized automorphism ensemble decoding into an extended Tanner graph, allowing BP to jointly exploit automorphism structure and channel information without explicit per-path preprocessing losses. Empirical results show iGAED offers measurable improvements over GAED and stand-alone BP, with additional benefits under strict latency constraints and for certain code structures, sometimes approaching ML performance at high SNR. This approach provides a practical path toward flexible, low-latency decoding for future wireless systems (e.g., URLLC) by balancing complexity, throughput, and reliability through ensemble design and graph-based preprocessing integration.

Abstract

With the increasing demands on future wireless systems, new design objectives become eminent. Low-density parity-check codes together with belief propagation (BP) decoding have outstanding performance for large block lengths. Yet, for future wireless systems, good decoding performance for short block lengths is mandatory, a regime in which BP decoding typically shows a significant gap to maximum likelihood decoding. Automorphism ensemble decoding (AED) is known to reduce this gap effectively and, in addition, enables an easy trade-off between latency, throughput, and complexity. Recently, generalized AED (GAED) was proposed to increase the set of feasible automorphisms suitable for ensemble decoding. By construction, GAED requires a preprocessing step within its constituent paths that results in information loss and potentially limits the gains of GAED. In this work, we show that the preprocessing step can be merged with the Tanner graph of BP decoding, thereby improving the performance of the constituent paths. Finally, we show that the improvement of the individual paths also enhances the overall performance of the ensemble.

Figures (7)

• Figure 1: Block diagram of GAED introduced by mandelbaum2023generalized in which $K$ different automorphisms with transformation matrices ${\bm{T}_\ell }$ are used. We assume that each path performs BP decoding based on the PCM $\bm{H}$.
• Figure 2: Graphical illustration of the transformation of the conventional path from GAED in (a) via the merged Tanner graph in (b) to the pruned Tanner graph in (c).
• Figure 3: A path of iGAED using the pruned matrix $\bm{H}_{\text{iGAED,p}}$. The embedding maps the channel output to an extended LLR vector of dimension $2n$ by appending zeros.
• Figure 4: Performance of different decoders for code $\mathcal{C}_2(32,16)$ from mandelbaum2023generalized. Additionally, the stand-alone performance of the auxiliary paths of GAED--$3$--BP--$30$ and iGAED--$3$--BP--$30$ are depicted, respectively.
• Figure 5: Performance of different decoders for code $\mathcal{C}_3(63,45)$ from mandelbaum2023generalized. Additionally, the stand-alone performance of the auxiliary paths of GAED--$3$--BP--$30$ and iGAED--$3$--BP--$30$ are depicted, respectively.