Diagnosis of weaknesses in modern error correction codes: a physics approach

TL;DR

This paper introduces a physics-inspired instanton method to systematically analyze the bit-error-rate of modern error correction codes in weak noise conditions, where traditional methods struggle due to low error rates.

Contribution

It applies the instanton approach from physics to error correction codes, providing a new systematic way to characterize BER at weak noise levels.

Findings

Instanton method effectively estimates BER in weak noise regimes.

Recasts BER analysis as a minimization problem, simplifying computations.

Provides insights into decoding failures at low error rates.

Abstract

One of the main obstacles to the wider use of the modern error-correction codes is that, due to the complex behavior of their decoding algorithms, no systematic method which would allow characterization of the Bit-Error-Rate (BER) is known. This is especially true at the weak noise where many systems operate and where coding performance is difficult to estimate because of the diminishingly small number of errors. We show how the instanton method of physics allows one to solve the problem of BER analysis in the weak noise range by recasting it as a computationally tractable minimization problem.