In this paper, we first introduce the extended binary representation ofnon-binary codes, which corresponds to a covering graph of the bipartite graphassociated with the non-binary code. Then we show that non-binary codewordscorrespond to binary codewords of the extended representation that furthersatisfy some simplex-constraint: that is, bits lying over the same symbol-nodeof the non-binary graph must form a codeword of a simplex code. Applied to thebinary erasure channel, this description leads to a binary erasure decodingalgorithm of non-binary LDPC codes, whose complexity depends linearly on thecardinality of the alphabet. We also give insights into the structure ofstopping sets for non-binary LDPC codes, and discuss several aspects related toupper-layer FEC applications.
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