Performance of LDPC Codes Under Faulty Iterative Decoding

TL;DR

This paper investigates how noise in both circuits and communication channels affects the performance of iterative decoders for LDPC codes, revealing that noise degrades decoding thresholds but zero-error probability may still be achievable under certain models.

Contribution

It introduces models for faulty iterative decoding, derives density evolution equations under noise, and provides new insights into the limits of reliable decoding with noisy hardware.

Findings

Decoding performance concentrates around its average despite noise.

Performance degrades smoothly as decoder noise increases.

Zero-error probability is achievable in some noisy models.

Abstract

Departing from traditional communication theory where decoding algorithms are assumed to perform without error, a system where noise perturbs both computational devices and communication channels is considered here. This paper studies limits in processing noisy signals with noisy circuits by investigating the effect of noise on standard iterative decoders for low-density parity-check codes. Concentration of decoding performance around its average is shown to hold when noise is introduced into message-passing and local computation. Density evolution equations for simple faulty iterative decoders are derived. In one model, computing nonlinear estimation thresholds shows that performance degrades smoothly as decoder noise increases, but arbitrarily small probability of error is not achievable. Probability of error may be driven to zero in another system model; the decoding threshold again decreases smoothly with decoder noise. As an application of the methods developed, an achievability result for reliable memory systems constructed from unreliable components is provided.