Prior-Assisted Hierarchical ADMM Decoding for Punctured Globally Coupled LDPC Codes

. 2026 Jul 17;28(7):815. doi: 10.3390/e28070815

Algorithm 1 Online TPD-ADMM decoding for punctured GC-LDPC codes

Input:
Received LLR vector $γ$ ; local matrices $H_{1}, H_{2}$ ; complete matrix $H_{GC}$ ; tuned ADMM and prior-control parameters.
Output:
Final hard decision $\hat{x}$ .
1:
Extract $γ_{1}$ and $γ_{2}$ from the full-length LLR vector $γ$ .
2:
Run the local ADMM decoders on $(H_{1}, γ_{1})$ and $(H_{2}, γ_{2})$ in parallel to obtain $x_{1}^{L}, x_{2}^{L}$ and ${\hat{x}}_{1}^{L}, {\hat{x}}_{2}^{L}$ .
3:
Concatenate ${\hat{x}}_{1}^{L}$ and ${\hat{x}}_{2}^{L}$ to form ${\hat{x}}_{loc}$ and compute its syndrome using $H_{GC}$ .
4:
if $H_{GC} {\hat{x}}_{loc}^{T} = 0$ then
5:
Set $\hat{x} \leftarrow {\hat{x}}_{loc}$ .
6:
return $\hat{x}$ .
7:
end if
8:
Map $x_{1}^{L}$ and $x_{2}^{L}$ to pseudo-LLR priors.
9:
Apply local-confidence gating, magnitude clipping, and channel-conflict scaling.
10:
Fuse the controlled priors with $γ$ and run the global ADMM fallback decoder on $H_{GC}$ .
11:
Select $\hat{x}$ by complete-matrix validity; if both candidates are invalid, apply the lexicographic syndrome-weight and channel-metric rule.
12:
return $\hat{x}$ .