Weight distribution of low-density parity-check codes
We derive the average weight distribution function and its asymptotic growth rate for low-density parity-check (LDPC) code ensembles. We show that the growth rate of the minimum distance of LDPC codes depends only on the degree distribution pair. It turns out that capacity-achieving sequences of standard (unstructured) LDPC codes under iterative decoding over the binary erasure channel (BEC) known to date have sublinearly growing minimum distance in the block length.
weight distribution growth rate low-density parity-check (ldpc) codes minimum distance capacity-achieving sequences binary erasure channel (bec) irregular repeat-accumulate (ira) codes