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. 2026 Oct 14;28(10):1123. doi: 10.3390/e28101123
LDPC Low-density parity-check
QC Quasi-cyclic
BIBD Balanced incomplete block design
CPM Circulant permutation matrix
QC-LDPC Quasi-cyclic low-density parity-check
SPA Sum-product algorithm
Fp Finite field of order p
Fp* Multiplicative group of order p−1
G(p) A (3, 29)-regular bipartite graph
p ≡ 1 (modJL) Condition for existence of primitive JL-th root (for our parameters, JL = 87)
2h-cycle A cycle of length 2h
Φ87(x) 87th cyclotomic polynomial
GCD Greatest common divisor
S6 The prime set corresponding to girth 6
S8 The prime set corresponding to girth 8
S10 The prime set corresponding to girth 10
H Parity-check matrix
EXIT Extrinsic information transfer
VND Variable-node decoder
CND Check-node decoder
AWGN Additive white Gaussian noise
BPSK Binary phase shift keying
SNR Signal-to-noise ratio
BER Bit error rate
FER Frame error rate