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IEEE Transactions on Communications

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

Christiane L. Kameni Ngassa, Valentin Savin, Elsa Dupraz, David Declercq

Published Jan 6, 2015• 37 citations
Publisher

Abstract

This paper investigates the behavior of the Min-Sum decoder running on noisy devices. Our aim is to evaluate the robustness of the decoder to computation noise caused by the faulty logic in the processing units. This type of noise 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 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 point out a specific threshold phenomenon, referred to as functional threshold, which accurately describes the convergence behavior of noisy decoders. The behavior of the noisy MS is demonstrated in the asymptotic limit of the code length through a noisy version of density evolution and is also verified in the finite-length case by Monte Carlo simulations.

DOI
10.1109/tcomm.2015.2388472

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This paper investigates the behavior of the Min-Sum decoder running on noisy devices. Our aim is to evaluate the robustness of the decoder to computation noise caused by the faulty logic in the processing units. This type of noise 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 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 point out a specific threshold phenomenon, referred to as functional threshold, which accurately describes the convergence behavior of noisy decoders. The behavior of the noisy MS is demonstrated in the asymptotic limit of the code length through a noisy version of density evolution and is also verified in the finite-length case by Monte Carlo simulations.
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.
This paper investigates the behavior of the noisy Min-Sum decoder over binary symmetric channels. A noisy decoder is a decoder running on a noisy device, which may introduce errors during the decoding process. We show that in some particular cases, the noise introduce 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.
In this paper, we define Noise-against-Noise Min-Sum (NAN-MS) decoders as decoders that incorporate a certain amount of random perturbation due to deliberate noise injection. We introduce a noise model which is used to implement quantized NAN-MS decoders, using a limited number of precision bits. The behavior of NAN-MS decoders is investigated in the asymptotic limit of the code length using a noisy version of density evolution (DE). We use the noisy-DE thresholds to analyze and optimize the noise model parameters. We show that a controlled injection of noise allows NAN-MS decoders to achieve better performance than noiseless MS decoders, especially for low precision. The finite-length simulations confirm the conclusions of the DE analysis.
This paper deals with Low-Density Parity-Check decoders running on noisy hardware. This represents an unconventional paradigm in communication theory, since it is traditionally assumed that the error correction decoder operates on error-free devices and the randomness (in the form of noise and/or errors) exists only in the transmission channel. However, with the advent of nanoelectronics, it starts to be widely accepted that the future generations of circuits and systems will need to reliability compute and solve statistical inferences, by making use of unreliable “noisy” components. It is then critical to properly evaluate the robustness of the existing decoders in the presence of an additional source of noise at the circuit level. To this end, we first introduce a new error model approach and carry out the “noisy” density evolution analysis of the fixed-point Min-Sum decoding. Then, for different parameters of the noisy components of the decoder, we determine the range of the signal-to-noise ratio values for which the decoder is able to achieve a target bit error rate performance. Finally, we evaluate the finite-length performance of the Min-Sum and two other Min-Sum-based decoders running on noisy hardware.
In this paper, we analyze Finite Alphabet Iterative Decoders (FAIDs) running on faulty hardware. Under symmetric error models at the message level, we derive the noisy Density Evolution equations, and introduce a new noisy threshold phenomenon (called functional threshold), which accurately characterizes the convergence behavior of LDPC code ensembles under noisy-FAID decoding. The proposed functional threshold is then used to identify FAIDs which are particularly robust to the transient hardware noise. Finite-length simulations are drawn to verify the validity of the asymptotical study.
Motivated by the problem of designing fault-tolerant memories built out from unreliable components, this paper investigates the performance of two noisy Min-Sum-based decoders on Binary Symmetric Channels. We analyze the performance of the noisy Min-Sum decoder in terms of useful regions and target bit-error rate threshold values, derived by using “noisy” density evolution equations. We also present the finite length performance of two Min-Sum based decoders, and point out the excellent performance of the noisy Self-Corrected Min-Sum decoder, which exhibits almost the same performance as the noiseless decoder.