Low-Density Parity-Check Codes and Matrices

Find below a list of low-density parity-check (LDPC) codes (generating polynomials and thresholds) and matrices (in the alist format proposed by D. MacKay, M. Davey, and J. Lafferty) particularly optimized for different coding rates and communication channels.

Codes were computed using the discretized density evolution algorithm.

Matrices for different block lengths were constructed using the original progressive edge-growth (PEG) algorithm.

Additive White Gaussian Channel

Rate Generating Polynomials Threshold Matrices
0.5 λ(x) = 0.23802 x + 0.20997 x2 + 0.03492 x3 + 0.12015 x4 + 0.01587 x6 + 0.00480 x13 + 0.37627 x14 0.1493 N=104
ρ(x) = 0.98013 x7 + 0.01987 x8
    
0.6 λ(x) = 0.160608 x + 0.134533 x2 + 0.0482729 x3 + 0.0468901 x4 + 0.102275 x7 + 0.102575 x8 + 0.0454141 x10 + 0.359432 x44 0.829355 N=104
ρ(x) = 0.314523 x12 + 0.685477 x13
    

Binary Symmetric Channel

Rate Generating Polynomials Threshold Matrices
0.3 λ(x) = 0.247205 x + 0.225225 x2 + 0.0543745 x3 + 0.153518 x8 + 0.168646 x9 + 0.151032 x39 0.180247 N=104
ρ(x) = 0.24935 x4 + 0.75065 x5
    
0.4 λ(x) = 0.181749 x + 0.147329 x2 + 0.0544272 x3 + 0.0707276 x4 + 0.0686918 x6 + 0.135139 x8 + 0.159581 x34 + 0.182355 x39 0.140508 N=104
ρ(x) = 0.712734 x7 + 0.287266 x8
    
0.5 λ(x) = 0.159673 x + 0.121875 x2 + 0.11261 x3 + 0.190871 x4 + 0.0770616 x9 + 0.337909 x24 0.102592
N=2×103
N=104
N=105
N=2×105
ρ(x) = 0.360479 x8 + 0.639521 x9
    
0.6 λ(x) = 0.11653 x + 0.125646 x2 + 0.108507 x3 + 0.0534223 x4 + 0.0727228 x6 + 0.0347964 x7 + 0.0729986 x8 + 0.0752607 x17 + 0.117103 x31 + 0.223013 x44 0.0745261 N=104
N=105
N=2×105
ρ(x) = 0.582731 x13 + 0.417269 x14
    
0.7 λ(x) = 0.091699 x + 0.171401 x2 + 0.0683878 x3 + 0.120523 x4 + 0.187471 x10 + 0.208278 x27 + 0.152239 x29 0.0501875 N=104
N=105
N=2×105
ρ(x) = 0.806453 x18 + 0.193547 x19
    
0.8 λ(x) = 0.0667948 x  0.194832 x2 + 0.0570523 x3 + 0.0645024 x4 + 0.204606 x8 + 0.0964409 x14 + 0.23872 x28 + 0.0770523 x34 0.0289413 N=2×103
N=104
N=105
N=2×105
ρ(x) = 0.708874 x29 + 0.291126 x30