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

Yoni Choukroun, Lior Wolf

Keywords: ECC, Binary Programming, Belief Propagation

TL;DR: We learn new binary linear block codes by optimizing the factor graph of the Belief Propagation algorithm

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.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Submission Number: 4788