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Two iterative decoding algorithms of 3D-product block codes (3D-PBC) based on genetic algorithms (GAs) are presented. The first algorithm uses the Chase-Pyndiah SISO, and the second one uses the list-based SISO decoding algorithm (LBDA) based on order- reprocessing. We applied these algorithms over AWGN channel to symmetric 3D-PBC constructed from BCH codes. The simulation results show that the first algorithm outperforms the Chase-Pyndiah one and is only 1.38 dB away from the Shannon capacity limit at BER of 10−5 for BCH (31, 21, 5)3 and 1.4 dB for BCH (16, 11, 4)3. The simulations of the LBDA-based GA on the BCH (16, 11, 4)3 show that its performances outperform the first algorithm and is about 1.33 dB from the Shannon limit. Furthermore, these algorithms can be applied to any arbitrary 3D binary product block codes, without the need of a hard-in hard-out decoder. We show also that the two proposed decoders are less complex than both Chase-Pyndiah algorithm for codes with large correction capacity and LBDA for large  parameter. Those features make the decoders based on genetic algorithms efficient and attractive

Reduced Complexity Iterative Decoding of 3D-Product Block Codes Based on Genetic Algorithms