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Channel Codes by Shu Lin, William Ryan

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11Constructions of LDPC Codes Based on Finite Fields

In the late 1950s and early 1960s, finite fields were successfully used to construct linear block codes, especially cyclic codes, with large minimum distances for hard-decision algebraic decoding, such as BCH codes [1, 2] and RS codes [3]. There have recently been major developments in using finite fields to construct LDPC codes [411]. LDPC code constructions based on finite fields perform well over the binary-input AWGN channel with iterative decoding based on belief propagation. Most importantly, these finite-field LDPC codes were shown to have low error floors, which is important for communication and data-storage systems, for which very low bit and/or word error rates are required. Furthermore, ...

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