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Channel Codes by Shu Lin, William Ryan

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10Finite-Geometry LDPC Codes

Finite geometries, such as Euclidean and projective geometries, are powerful mathematical tools for constructing error-control codes. In the 1960s and 1970s, finite geometries were successfully used to construct many classes of easily implementable majority-logic decodable codes. In 2000, Kou, Lin, and Fossorier [13] showed that finite geometries can also be used to construct LDPC codes that perform well and close to the Shannon theoretical limit with iterative decoding based on belief propagation. These codes are called finite-geometry (FG)-LDPC codes. FG-LDPC codes form the first class of LDPC codes that are constructed algebraically. Since 2000, there have been many major developments in construction of LDPC codes ...

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