The approximate maximum-likelihood certificate

TL;DR

This paper introduces the approximate maximum-likelihood certificate (AMLC), a property based on LP decoding that enhances error detection by providing confidence bounds on decoding accuracy, especially in low-noise channels.

Contribution

The paper presents the AMLC property, linking LP decoding with belief propagation, and demonstrates its effectiveness in providing high-confidence error bounds without extensive simulations.

Findings

Conditional frame error probability is significantly lower when AMLC holds.

AMLC provides a reliable error detection mechanism in low-noise channels.

The approach reduces the need for long Monte Carlo simulations.

Abstract

A new property which relies on the linear programming (LP) decoder, the approximate maximum-likelihood certificate (AMLC), is introduced. When using the belief propagation decoder, this property is a measure of how close the decoded codeword is to the LP solution. Using upper bounding techniques, it is demonstrated that the conditional frame error probability given that the AMLC holds is, with some degree of confidence, below a threshold. In channels with low noise, this threshold is several orders of magnitude lower than the simulated frame error rate, and our bound holds with very high degree of confidence. In contrast, showing this error performance by simulation would require very long Monte Carlo runs. When the AMLC holds, our approach thus provides the decoder with extra error detection capability, which is especially important in applications requiring high data integrity.