Chenyuan Jia | Searcharxiv

arXiv2026

Dynamic Layered Decoding Scheduling for LDPC Codes Aided by Check Node Unsatisfied Probabilities

This letter revisits update ordering in layered belief propagation (LBP) decoding of low-density parity-check (LDPC) codes. The closest probability-based schedule orders layers by check node unsatisfied probabilities estimated only from the channel observations, although these probabilities change once decoding messages are exchanged. We therefore refresh the check node unsatisfied probabilities during decoding and use them as dynamic priorities. The first schedule, Dyn-EBP, selects the most reliable available check node while ensuring that every check node is updated once in each iteration. The second schedule, Dyn-PEBP, adds a linear update-count penalty and allows limited repeated updates without letting a small subset of check nodes dominate the schedule. For 5G new radio LDPC base graph 1 codes with five iterations, the proposed schedules yield small BLER reductions relative to the channel-only probability schedule and remain competitive with LBP, LPHD scheduling, and RD-RBP. The gain is modest, but it shows that probability-based scheduling benefits from message-level refinement.

cs.IT↗

arXiv2026

On the Intractability of the Minimum Distance Problem for Regular LDPC Codes

The minimum distance problem (MDP) for low-density parity-check (LDPC) codes is a central problem in coding theory and is closely related to the analysis of low-weight codewords and error-floor behavior. Although the unrestricted MDP is computationally intractable, its complexity under degree constraints that commonly occur in LDPC code design has remained less clear. In this paper, we study the MDP for left regular and biregular Tanner graphs. For every fixed $J\geq3$, we prove that the standard at-most-weight problem is $\mathrm{NP}$-complete for $J$-left regular Tanner graphs and that its exact-weight variant is $\mathrm{W}[1]$-complete when parameterized by the prescribed weight. For biregular Tanner graphs, we prove $\mathrm{NP}$-completeness for $(3,K)$-regular instances for every fixed $K\geq 3$ by replacing degree-two auxiliary completion blocks with a single-port high-girth gadget. A nonzero relative support inside this gadget induces an essentially cubic graph, so the Moore bound gives an exponential lower bound in the girth and allows a polynomial-size Karp reduction. Combining this right-degree amplification with a replica-and-global-check left-degree amplification yields $\mathrm{NP}$-completeness for $(J,K)$-regular Tanner graphs for every fixed $J,K\geq 3$. The reductions are based on a degree-preserving transformation framework consisting of hyperedge decomposition, check node splitting, and controlled variable replication. These transformations relate different degree distributions while preserving explicit maps among nonzero codewords, even covers, and nonempty $(a,0)$-trapping sets. The results delineate the computational limits of computing minimum distance exactly under natural regularity constraints.

cs.CC↗