The Sum-Product Algorithm for Degree-2 Check Nodes and Trapping Sets

TL;DR

This paper analyzes the sum-product decoding algorithm for bipartite graphs with degree-2 check nodes, simplifying it to linear algebra, and investigates its convergence and trapping set behavior.

Contribution

It provides a simplified linear algebraic formulation of the sum-product algorithm for degree-2 check nodes and derives exact convergence results.

Findings

Simplified sum-product algorithm for degree-2 check nodes

Exact convergence conditions derived

Insights into trapping set behavior

Abstract

The sum-product algorithm for decoding of binary codes is analyzed for bipartite graphs in which the check nodes all have degree $2$. The algorithm simplifies dramatically and may be expressed using linear algebra. Exact results about the convergence of the algorithm are derived and applied to trapping sets.