Abstract

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.KeywordsZeta FunctionLDPC CodeCheck NodeIterative DecodeSimplicial ConeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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