Algorithms for Enumerating Balanced Tanner Graphs

TL;DR

This paper presents new algorithms for enumerating Balanced Tanner Graphs, focusing on cyclic permutation group-based methods and a constrained algorithm for graphs with larger minimum cycle lengths.

Contribution

It introduces novel enumeration algorithms for Balanced Tanner Graphs, including a constrained method for graphs with larger minimum cycles, advancing the understanding of their structure.

Findings

Developed enumeration algorithms based on cyclic permutation groups.

Described a constrained enumeration algorithm for graphs with larger minimum cycles.

Enhanced the understanding of Balanced Tanner Graphs' structural properties.

Abstract

This summarizes our latest understanding and results about the algorithms for enumerating Tanner Graphs that have a regular structure called Balanced Tanner Graphs. Enumeration algorithms for Balanced Tanner Graphs based upon Cyclic Permutation Groups have been developed in this paper. A constrained enumeration algorithm that enumerates Balanced Tanner Graphs that have a relatively larger length of minimum cycle has been described.