1,003 research outputs found
The Dynamic Phase Transition for Decoding Algorithms
The state-of-the-art error correcting codes are based on large random
constructions (random graphs, random permutations, ...) and are decoded by
linear-time iterative algorithms. Because of these features, they are
remarkable examples of diluted mean-field spin glasses, both from the static
and from the dynamic points of view. We analyze the behavior of decoding
algorithms using the mapping onto statistical-physics models. This allows to
understand the intrinsic (i.e. algorithm independent) features of this
behavior.Comment: 40 pages, 29 eps figure
Binary Message Passing Decoding of Product-like Codes
We propose a novel binary message passing decoding algorithm for product-like
codes based on bounded distance decoding (BDD) of the component codes. The
algorithm, dubbed iterative BDD with scaled reliability (iBDD-SR), exploits the
channel reliabilities and is therefore soft in nature. However, the messages
exchanged by the component decoders are binary (hard) messages, which
significantly reduces the decoder data flow. The exchanged binary messages are
obtained by combining the channel reliability with the BDD decoder output
reliabilities, properly conveyed by a scaling factor applied to the BDD
decisions. We perform a density evolution analysis for generalized low-density
parity-check (GLDPC) code ensembles and spatially coupled GLDPC code ensembles,
from which the scaling factors of the iBDD-SR for product and staircase codes,
respectively, can be obtained. For the white additive Gaussian noise channel,
we show performance gains up to dB and dB for product and
staircase codes compared to conventional iterative BDD (iBDD) with the same
decoder data flow. Furthermore, we show that iBDD-SR approaches the performance
of ideal iBDD that prevents miscorrections.Comment: Accepted for publication in the IEEE Transactions on Communication
Information- and Coding-Theoretic Analysis of the RLWE Channel
Several cryptosystems based on the \emph{Ring Learning with Errors} (RLWE)
problem have been proposed within the NIST post-quantum cryptography
standardization process, e.g. NewHope. Furthermore, there are systems like
Kyber which are based on the closely related MLWE assumption. Both previously
mentioned schemes feature a non-zero decryption failure rate (DFR). The
combination of encryption and decryption for these kinds of algorithms can be
interpreted as data transmission over noisy channels. To the best of our
knowledge this paper is the first work that analyzes the capacity of this
channel. We show how to modify the encryption schemes such that the input
alphabets of the corresponding channels are increased. In particular, we
present lower bounds on their capacities which show that the transmission rate
can be significantly increased compared to standard proposals in the
literature. Furthermore, under the common assumption of stochastically
independent coefficient failures, we give lower bounds on achievable rates
based on both the Gilbert-Varshamov bound and concrete code constructions using
BCH codes. By means of our constructions, we can either increase the total
bitrate (by a factor of for Kyber and by factor of for NewHope)
while guaranteeing the same \emph{decryption failure rate} (DFR). Moreover, for
the same bitrate, we can significantly reduce the DFR for all schemes
considered in this work (e.g., for NewHope from to ).Comment: 13 pages, 4 figures, 3 table
Instantly Decodable Network Coding: From Centralized to Device-to-Device Communications
From its introduction to its quindecennial, network coding has built a strong reputation for enhancing packet recovery and achieving maximum information flow in both wired and wireless networks. Traditional studies focused on optimizing the throughput of the system by proposing elaborate schemes able to reach the network capacity. With the shift toward distributed computing on mobile devices, performance and complexity become both critical factors that affect the efficiency of a coding strategy. Instantly decodable network coding presents itself as a new paradigm in network coding that trades off these two aspects. This paper review instantly decodable network coding schemes by identifying, categorizing, and evaluating various algorithms proposed in the literature. The first part of the manuscript investigates the conventional centralized systems, in which all decisions are carried out by a central unit, e.g., a base-station. In particular, two successful approaches known as the strict and generalized instantly decodable network are compared in terms of reliability, performance, complexity, and packet selection methodology. The second part considers the use of instantly decodable codes in a device-to-device communication network, in which devices speed up the recovery of the missing packets by exchanging network coded packets. Although the performance improvements are directly proportional to the computational complexity increases, numerous successful schemes from both the performance and complexity viewpoints are identified
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