Low-Density Parity-Check (LDPC) codes are linear block error-correcting codes specified by an extremely sparse parity-check matrix H. Represented graphically by a bipartite Tanner graph linking Variable Nodes (codeword bits) to Check Nodes (parity constraints), LDPC decoding operates via the iterative sum-product (belief propagation) algorithm, exchanging probability messages along edges to achieve capacity-approaching error performance in 5G NR and DVB-S2 satellite links.