In this paper we prove two results related to low-density parity-check (LDPC) codes. The first is to show that the generating function attached to the pseudo-codewords of an LDPC code is a rational function, answering a question raised in [6]. The combinatorial information of its numerator and denominator is also discussed. The second concerns an infinite family of q-regular bipartite graphs with large girth constructed in [8]. The LDPC codes based on these graphs have attracted much attention. We show that the first few of these graphs are Ramanujan graphs. © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Li, W. C. W., Lu, M., & Wang, C. (2009). Recent developments in low-density parity-check codes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5557 LNCS, pp. 107–123). https://doi.org/10.1007/978-3-642-01877-0_11
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