2009/10/10 by Valentin Savin, Savin, Valentin · 1 citation
Computer Science · Engineering · #Advanced Wireless Communication Techniques #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #Telecommunications and Broadcasting Technologies
paper · pdf · doi:10.48550/arxiv.0910.1922
openalex publication_date 2009/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we first introduce the extended binary representation of non-binary codes, which corresponds to a covering graph of the bipartite graph associated with the non-binary code. Then we show that non-binary codewords correspond to binary codewords of the extended representation that further satisfy some simplex-constraint: that is, bits lying over the same symbol-node of the non-binary graph must form a codeword of a simplex code. Applied to the binary erasure channel, this description leads to a binary erasure decoding algorithm of non-binary LDPC codes, whose complexity depends linearly on the cardinality of the alphabet. We also give insights into the structure of stopping sets for non-binary LDPC codes, and discuss several aspects related to upper-layer FEC applications.