Titlebook: Error-Correction Coding and Decoding; Bounds, Codes, Decod Martin Tomlinson,Cen Jung Tjhai,Mubarak Jibril Book‘‘‘‘‘‘‘‘ 2017 The Editor(s) (

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Jacob Acontius: From Trent to , (1565),utperformed the LDPC and Turbo systems. To date, for the AWGN channel and net, half rate codes no other codes or coding arrangement is known that will outperform the system presented in this chapter for codes of lengths 256 and 512 bits.

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Lagrange Codesis shown how Goppa codes and BCH codes may be extended in length with additional parity check bits resulting in increased minimum Hamming distance of the code. Several examples are given of the technique which results in some exceptional codes. Reed–Solomon codes are explored as a means of construct

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A Concatenated Error-Correction System Using the , Code Constructionutperformed the LDPC and Turbo systems. To date, for the AWGN channel and net, half rate codes no other codes or coding arrangement is known that will outperform the system presented in this chapter for codes of lengths 256 and 512 bits.

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Bounds on Error-Correction Coding Performancem for binary codes is treated extensively. By assuming a binomial weight distribution for linear codes, it is shown that the decoder error probability performance of some of the best, known linear, binary codes is the same as the average performance of the ensemble of all randomly chosen, binary non