Density Evolution and Functional Threshold for the Noisy Min-Sum Decoder

TL;DR

This paper analyzes the robustness of the Min-Sum decoder under device noise, introducing probabilistic models and density evolution analysis to understand how noise impacts decoding performance and reveals a functional threshold phenomenon.

Contribution

It introduces probabilistic models for noisy arithmetic units and density evolution analysis for the Min-Sum decoder under noise, revealing a noise-induced threshold behavior.

Findings

Noise can help escape fixed points, improving correction capacity.

Existence of a functional threshold in noisy decoding.

Validation through asymptotic analysis and finite-length simulations.

Abstract

This paper investigates the behavior of the Min-Sum decoder running on noisy devices. The aim is to evaluate the robustness of the decoder in the presence of computation noise, e.g. due to faulty logic in the processing units, which represents a new source of errors that may occur during the decoding process. To this end, we first introduce probabilistic models for the arithmetic and logic units of the the finite-precision Min-Sum decoder, and then carry out the density evolution analysis of the noisy Min-Sum decoder. We show that in some particular cases, the noise introduced by the device can help the Min-Sum decoder to escape from fixed points attractors, and may actually result in an increased correction capacity with respect to the noiseless decoder. We also reveal the existence of a specific threshold phenomenon, referred to as functional threshold. The behavior of the noisy decoder is demonstrated in the asymptotic limit of the code-length -- by using "noisy" density evolution equations -- and it is also verified in the finite-length case by Monte-Carlo simulation.