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Channel Codes by Shu Lin, William Ryan

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12LDPC Codes Based on Combinatorial Designs, Graphs, and Superposition

Combinatorial designs [18] form an important branch in combinatorial mathematics. In the late 1950s and during the 1960s, special classes of combinatorial designs, such as balanced incomplete block designs, were used to construct error-correcting codes, especial majority-logic-decodable codes. More recently, combinatorial designs were successfully used to construct structured LDPC codes [912]. LDPC codes of practical lengths constructed from several classes of combinatorial designs were shown to perform very well over the binary-input AWGN channel with iterative decoding.

Graphs form another important branch in combinatorial mathematics. They were also used to construct ...

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