A Mathematical Approach to Balanced Tanner Graph Enumeration

TL;DR

This paper explores a mathematical framework for enumerating Balanced Tanner Graphs, providing theoretical insights and raising open questions in the field of graph enumeration within coding theory.

Contribution

It introduces a novel mathematical approach to enumerate Balanced Tanner Graphs, combining permutation group theory with enumeration theorems.

Findings

Presented permutation group preliminaries relevant to Tanner Graphs

Developed enumeration theorems for Balanced Tanner Graphs

Outlined an approach and identified open questions in the enumeration process

Abstract

This paper summarizes our latest understanding and results about the application of the Mathematics Of Enumeration to Tanner Graphs that have a regular structure called Balanced Tanner Graphs. Some preliminaries of permutation groups have been presented followed by various enumeration theorems, and finally our approach for enumeration of Balanced Tanner Graphs has been explained, and several open questions have been raised.