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Performance comparison of message passing decoding algorithms for binary and non-binary low density parity check (LDPC) codes

Uzunoğlu, Cihan
In this thesis, we investigate the basics of Low-Density Parity-Check (LDPC) codes over binary and non-binary alphabets. We especially focus on the message passing decoding algorithms, which have different message definitions such as a posteriori probabilities, log-likelihood ratios and Fourier transforms of probabilities. We present the simulation results that compare the performances of small block length binary and non-binary LDPC codes, which have regular and irregular structures over GF(2),GF(4) and GF(8) alphabets. We observe that choosing non-binary alphabets improve the performance with careful selection of mean column weight by comparing LDPC codes with variable node degrees of 3, 2.8 and 2.6, since it is effective in the order of GF(2), GF(4) and GF(8) performances.