Computing the Minimum Distance of Nonbinary LDPC Codes

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Finding the minimum distance of Low-Density Parity-Check (LDPC) codes is an NP-hard problem. Different from all existing works that focus on binary LDPC codes, the authors in this paper aim to compute the minimum distance of non-binary LDPC codes, motivated by the fact that operating in a large Galois field provides one important degree of freedom to achieve both good waterfall and error-floor performance. Their method is based on the existing Nearest Non-zero Codeword Search (NNCS) method, but several modifications are incorporated for non-binary LDPC codes, including the modified error impulse pattern, the dithering method, and the non-binary decoder.