19 research outputs found
Faulty Successive Cancellation Decoding of Polar Codes for the Binary Erasure Channel
We study faulty successive cancellation decoding of polar codes for the
binary erasure channel. To this end, we introduce a simple erasure-based fault
model and we show that, under this model, polarization does not happen, meaning
that fully reliable communication is not possible at any rate. Moreover, we
provide numerical results for the frame erasure rate and bit erasure rate and
we study an unequal error protection scheme that can significantly improve the
performance of the faulty successive cancellation decoder with negligible
overhead.Comment: As presented at ISITA 201
Coding with Encoding Uncertainty
We study the channel coding problem when errors and uncertainty occur in the
encoding process. For simplicity we assume the channel between the encoder and
the decoder is perfect. Focusing on linear block codes, we model the encoding
uncertainty as erasures on the edges in the factor graph of the encoder
generator matrix. We first take a worst-case approach and find the maximum
tolerable number of erasures for perfect error correction. Next, we take a
probabilistic approach and derive a sufficient condition on the rate of a set
of codes, such that decoding error probability vanishes as blocklength tends to
infinity. In both scenarios, due to the inherent asymmetry of the problem, we
derive the results from first principles, which indicates that robustness to
encoding errors requires new properties of codes different from classical
properties.Comment: 12 pages; a shorter version of this work will appear in the
proceedings of ISIT 201
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
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
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
Noise facilitation in associative memories of exponential capacity
Recent advances in associative memory design through structured pattern sets and graph-based inference al- gorithms have allowed reliable learning and recall of an exponential number of patterns. Although these designs correct external errors in recall, they assume neurons that compute noiselessly, in contrast to the highly variable neurons in brain regions thought to operate associatively such as hippocampus and olfactory cortex. Here we consider associative memories with noisy internal computations and analytically characterize performance. As long as the internal noise level is below a specified threshold, the error probability in the recall phase can be made exceedingly small. More surprisingly, we show that internal noise actually improves the performance of the recall phase while the pattern retrieval capacity remains intact, i.e., the number of stored patterns does not reduce with noise (up to a threshold). Computational experiments lend additional support to our theoretical analysis. This work suggests a functional benefit to noisy neurons in biological neuronal networks