General Description

Low Density Parity Check (LDPC) codes are a class of linear block ECC that provide near-capacity performance. They utilize sparse encoding matrices and relatively large block sizes (typically, the number of \(1\)’s is linear in \(n\)). They are widely used in standards, for instance:

• IEEE802.3an-2006 (10GBASE-T Ethernet over copper wires)
• DVB-S2 (video broadcasts)
• IEEE.802.11n & IEEE.802.11ac (Wi-Fi standards 5&6). Here the use is optional in the HT (high throughput)
• specification, where they replace convolutional codes otherwise used.
• The codes will also be used in the 5G cellular standard.

From a historical point of view, the codes were initially invented by Gallager in 1960 and were later forgotten as they weren’t technologically viable at the time. Later, in 1981 Tanner found a generalized representation of the codes in the form of Tanner graphs. Further studies by Niel, Mackay, and others followed in the 1990s, at which point the codes were eventually used.