Low-density parity-check code

A linear error-correcting code defined by a sparse parity-check matrix. Its sparse structure enables efficient decoding while supporting performance close to channel capacity.

Parity-check matrix: A binary matrix whose null space contains the codewords of a linear code. Its low density is the defining structural feature of an LDPC code.
Linear code: A code whose valid words form a vector subspace over a finite field. Every binary LDPC code is a linear code with additional sparsity in its checks.
Robert Gallager: An American information theorist who introduced low-density parity-check codes in his 1960 doctoral work. Gallager developed the code family and its iterative decoding methods.
5G NR: The fifth-generation New Radio standard for cellular wireless communication. 5G NR uses LDPC codes for data-channel error correction.
Reed–Solomon code: A nonbinary error-correcting code that corrects symbol errors using polynomial evaluation over a finite field. It corrects burst errors effectively but usually lacks LDPC’s iterative sparse-graph decoding.
Tanner graph: A bipartite graph representing a code’s parity-check matrix with variable nodes and check nodes. It turns sparse matrix constraints into the graph used by iterative decoding.
Hamming weight: The number of nonzero symbols in a vector or codeword. Row and column weights quantify the sparsity of an LDPC parity-check matrix.
Information theory: The mathematical study of quantifying, storing, and communicating information. LDPC codes arose from the problem of reliable communication at high rates.
DVB-S2: A digital video broadcasting standard for satellite transmission. Its forward-error-correction system uses LDPC codes paired with BCH codes.
Convolutional code: A code that produces output symbols from a sliding window of input symbols and encoder state. Its trellis-based decoding differs from LDPC’s sparse-constraint message passing.

Linked from 7 pages