LDPC Codes

Abstract

LDPC codes are linear block codes whose parity-check matrix-as the name implies-is sparse. These codes can be iteratively decoded using the sum product [9] or equivalently the belief propagation [24] soft decision decoder. It has been shown, for example by Chung et al. [3], that for long block lengths, the performance of LDPC codes is close to the channel capacity. The theory of LDPC codes is related to a branch of mathematics called graph theory. Some basic definitions used in graph theory are briefly introduced as follows. Definition 12.1 (Vertex, Edge, Adjacent and Incident) A graph, denoted by G(V, E), consists of an ordered set of vertices and edges. • (Vertex) A vertex is commonly drawn as a node or a dot.