On the Dynamics of the Error Floor Behavior in (Regular) LDPC Codes

TL;DR

This paper analyzes the dynamic behavior of absorption sets in regular LDPC codes during iterative decoding, providing a model that predicts error floor performance and identifies key trapping set topologies.

Contribution

It introduces a linear dynamic model for absorption sets, enabling accurate error floor predictions and detailed topological analysis of dominant trapping sets.

Findings

Absorption sets undergo a two-phase dynamic behavior during decoding.

The model accurately predicts error floor bit error rates.

Topological relationships help identify dominant trapping sets.

Abstract

It is shown that dominant trapping sets of regular LDPC codes, so called absorption sets, undergo a two-phased dynamic behavior in the iterative message-passing decoding algorithm. Using a linear dynamic model for the iteration behavior of these sets, it is shown that they undergo an initial geometric growth phase which stabilizes in a final bit-flipping behavior where the algorithm reaches a fixed point. This analysis is shown to lead to very accurate numerical calculations of the error floor bit error rates down to error rates that are inaccessible by simulation. The topology of the dominant absorption sets of an example code, the IEEE 802.3an (2048,1723) regular LDPC code, are identified and tabulated using topological relationships in combination with search algorithms.