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In this paper we give a comparative analysis of decoding algorithms of Low Density Parity Check (LDPC) codes in a channel with the Nakagami distribution of the fading envelope. We consider the Progressive Edge-Growth (PEG) method and Improved PEG method for the parity check matrix construction, which can be used to avoid short girths, small trapping sets and a high level of error floor. A comparative analysis of several classes of LDPC codes in various propagation conditions and decoded using different decoding algorithms is also presented.