'Institute of Electrical and Electronics Engineers (IEEE)'
Abstract
In this paper the exponential growth rate of irregular generalized low-density parity-check (GLDPC) codes weight
distribution is considered. Specifically, the Taylor series of the
growth rate is expanded to the first order with the purpose of
studying its behavior in correspondence with the small weight
codewords. It is proved that the linear term of the Taylor
series, and then the expected number of small linear-sized weight
codewords of a randomly chosen GLDPC code in the irregular
ensemble, is dominated by the degree-2 variable nodes and by
the check nodes with minimum distance 2. A parameter is
introduced, only depending on such variable and check nodes,
discriminating between an exponentially small and exponentially
large expected number of small weight codewords