Cutsize Distributions of Balanced Hypergraph Bipartitions for Random Hypergraphs

TL;DR

This paper analyzes the distribution of minimum cutsize in balanced hypergraph bipartitions of random hypergraphs, revealing how it influences the processing time of a parallel encoding algorithm for LDPC codes.

Contribution

It provides the first detailed analysis of cutsize distributions in balanced hypergraph bipartitions for random hypergraphs, linking these to encoding efficiency.

Findings

Typical minimum cutsize values for random hypergraphs

Distribution patterns of cutsize in balanced bipartitions

Impact of cutsize on encoding processing time

Abstract

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.