952 research outputs found
Analysis and Design of Finite Alphabet Iterative Decoders Robust to Faulty Hardware
This paper addresses the problem of designing LDPC decoders robust to
transient errors introduced by a faulty hardware. We assume that the faulty
hardware introduces errors during the message passing updates and we propose a
general framework for the definition of the message update faulty functions.
Within this framework, we define symmetry conditions for the faulty functions,
and derive two simple error models used in the analysis. With this analysis, we
propose a new interpretation of the functional Density Evolution threshold
previously introduced, and show its limitations in case of highly unreliable
hardware. However, we show that under restricted decoder noise conditions, the
functional threshold can be used to predict the convergence behavior of FAIDs
under faulty hardware. In particular, we reveal the existence of robust and
non-robust FAIDs and propose a framework for the design of robust decoders. We
finally illustrate robust and non-robust decoders behaviors of finite length
codes using Monte Carlo simulations.Comment: 30 pages, submitted to IEEE Transactions on Communication
Spatially-Coupled LDPC Codes for Decode-and-Forward Relaying of Two Correlated Sources over the BEC
We present a decode-and-forward transmission scheme based on
spatially-coupled low-density parity-check (SC-LDPC) codes for a network
consisting of two (possibly correlated) sources, one relay, and one
destination. The links between the nodes are modeled as binary erasure
channels. Joint source-channel coding with joint channel decoding is used to
exploit the correlation. The relay performs network coding. We derive
analytical bounds on the achievable rates for the binary erasure time-division
multiple-access relay channel with correlated sources. We then design bilayer
SC-LDPC codes and analyze their asymptotic performance for this scenario. We
prove analytically that the proposed coding scheme achieves the theoretical
limit for symmetric channel conditions and uncorrelated sources. Using density
evolution, we furthermore demonstrate that our scheme approaches the
theoretical limit also for non-symmetric channel conditions and when the
sources are correlated, and we observe the threshold saturation effect that is
typical for spatially-coupled systems. Finally, we give simulation results for
large block lengths, which validate the DE analysis.Comment: IEEE Transactions on Communications, to appea
Faulty Successive Cancellation Decoding of Polar Codes for the Binary Erasure Channel
In this paper, faulty successive cancellation decoding of polar codes for the
binary erasure channel is studied. To this end, a simple erasure-based fault
model is introduced to represent errors in the decoder and it is shown that,
under this model, polarization does not happen, meaning that fully reliable
communication is not possible at any rate. Furthermore, a lower bound on the
frame error rate of polar codes under faulty SC decoding is provided, which is
then used, along with a well-known upper bound, in order to choose a
blocklength that minimizes the erasure probability under faulty decoding.
Finally, an unequal error protection scheme that can re-enable asymptotically
erasure-free transmission at a small rate loss and by protecting only a
constant fraction of the decoder is proposed. The same scheme is also shown to
significantly improve the finite-length performance of the faulty successive
cancellation decoder by protecting as little as 1.5% of the decoder.Comment: Accepted for publications in the IEEE Transactions on Communication
Density Evolution and Functional Threshold for the Noisy Min-Sum Decoder
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.Comment: 46 pages (draft version); extended version of the paper with same
title, submitted to IEEE Transactions on Communication
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