  In a previous work, we presented a parallel encoding algorithm for
low-density parity-check (LDPC) codes by partitioning hypergraph representation
for the LDPC codes. The aim of this research is to analyze the processing time
of this encoding algorithm. This paper clarifies that the processing time of
the encoding algorithm depends on the minimum cutsize of balanced hypergraph
partitions. Moreover, this paper gives the typical minimum cutsize and cutsize
distribution for balanced hypergraph bipartitions of random hypergraphs defined
from a regular LDPC ensemble.
