Low Density Parity Check (LDPC) codes belong to the class of forward error correction codes which are used for sending a message over noisy transmission channels. These codes can be described by a parity-check matrix which contains mostly 0's and a relatively small amount of 1's. Thus, the decoding complexity is small when compared to other code constructions. A very efficient iterative decoding algorithm is known as belief propagation (BP) decoder.
Therefore, LDPC codes are widely used as a powerful forward error correction (FEC) in nowadays communication standards such as Wifi (802.11n) or the WiMAX standard.
LDPC Codes can be divided into two types:
• Regular LDPC Codes: An LDPC code is called regular if the column weight $w_c$ and the row weight $w_r$ is constant.
• Irregular LDPC Codes: An LDPC code is called irregular if the column weight $w_c$ and the row weight $w_r$ is not constant. This means the number of 1's per row and column is not constant.
The second possibility is a graphical representation, so called Tanner Graph (see next slide).