Instanton-based Techniques for Analysis and Reduction of Error Floors of LDPC Codes

TL;DR

This paper introduces instanton-based optimization methods to analyze and reduce error floors in LDPC codes across various channels and decoders, providing insights into their topological structures and ways to design more robust codes.

Contribution

It develops a broad application of instanton analysis for LDPC error floors and proposes a method to design codes with improved performance by eliminating critical topological structures.

Findings

Instantons are the most probable noise configurations causing decoding failures.

The topological structures of instantons are related across different channels and decoders.

Constructed codes with Tanner graphs free of these structures exhibit lower error floors.

Abstract

We describe a family of instanton-based optimization methods developed recently for the analysis of the error floors of low-density parity-check (LDPC) codes. Instantons are the most probable configurations of the channel noise which result in decoding failures. We show that the general idea and the respective optimization technique are applicable broadly to a variety of channels, discrete or continuous, and variety of sub-optimal decoders. Specifically, we consider: iterative belief propagation (BP) decoders, Gallager type decoders, and linear programming (LP) decoders performing over the additive white Gaussian noise channel (AWGNC) and the binary symmetric channel (BSC). The instanton analysis suggests that the underlying topological structures of the most probable instanton of the same code but different channels and decoders are related to each other. Armed with this understanding of the graphical structure of the instanton and its relation to the decoding failures, we suggest a method to construct codes whose Tanner graphs are free of these structures, and thus have less significant error floors.