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Channel Codes by Shu Lin, William Ryan

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14Nonbinary LDPC Codes

Although a great deal of research effort has been expended on the design, construction, encoding, decoding, performance analysis, and applications of binary LDPC codes in communication and storage systems, very little has been done on non-binary LDPC codes in these respects. The first study of nonbinary LDPC codes was conducted by Davey and MacKay in 1998 [1]. In their paper, they generalized the SPA for decoding binary LDPC codes to decode q-ary LDPC codes, called QSPA. Later, in 2000, MacKay and Davey introduced a fast-Fourier-transform (FFT)-based QSPA to reduce the decoding computational complexity of QSPA [2]. This decoding algorithm is referred to as FFT-QSPA. MacKay and Davey’s work on FFT-QSPA was further improved ...

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