How are LDPC codes designed and decoded?

LDPC (Low-Density Parity-Check) codes are linear block codes defined by sparse parity-check matrix H. Design: Regular codes have fixed column/row weights; irregular codes optimize degree distribution for better threshold (using density evolution or EXIT chart analysis). Matrix construction: Random (capacity-approaching but high floor), structured (QC-LDPC for efficient implementation). Decoding: Belief propagation (sum-product algorithm) iteratively passes messages between variable and check nodes. Implementation uses min-sum approximation for complexity reduction. LDPC achieves within 0.1dB of Shannon limit and is used in DVB-S2, Wi-Fi 6, and 5G NR.