Factor Graph Optimization of Error-Correcting Codes for Belief Propagation Decoding

TL;DR

This paper introduces a novel gradient-based, data-driven method for designing sparse error-correcting codes optimized for belief propagation decoding, significantly improving performance over existing codes.

Contribution

It develops a new complete graph tensor representation of belief propagation and employs backpropagation to optimize code design, a first in the field.

Findings

Outperforms existing codes by orders of magnitude in decoding performance

Demonstrates the effectiveness of data-driven, gradient-based code design methods

Provides a new framework for optimizing codes under channel noise simulations

Abstract

The design of optimal linear block codes capable of being efficiently decoded is of major concern, especially for short block lengths. As near capacity-approaching codes, Low-Density Parity-Check (LDPC) codes possess several advantages over other families of codes, the most notable being its efficient decoding via Belief Propagation. While many LDPC code design methods exist, the development of efficient sparse codes that meet the constraints of modern short code lengths and accommodate new channel models remains a challenge. In this work, we propose for the first time a gradient-based data-driven approach for the design of sparse codes. We develop locally optimal codes with respect to Belief Propagation decoding via the learning of the Factor graph under channel noise simulations. This is performed via a novel complete graph tensor representation of the Belief Propagation algorithm, optimized over finite fields via backpropagation and coupled with an efficient line-search method. The proposed approach is shown to outperform the decoding performance of existing popular codes by orders of magnitude and demonstrates the power of data-driven approaches for code design.