1,462 research outputs found
Adaptive Protocols for Interactive Communication
How much adversarial noise can protocols for interactive communication
tolerate? This question was examined by Braverman and Rao (IEEE Trans. Inf.
Theory, 2014) for the case of "robust" protocols, where each party sends
messages only in fixed and predetermined rounds. We consider a new class of
non-robust protocols for Interactive Communication, which we call adaptive
protocols. Such protocols adapt structurally to the noise induced by the
channel in the sense that both the order of speaking, and the length of the
protocol may vary depending on observed noise.
We define models that capture adaptive protocols and study upper and lower
bounds on the permissible noise rate in these models. When the length of the
protocol may adaptively change according to the noise, we demonstrate a
protocol that tolerates noise rates up to . When the order of speaking may
adaptively change as well, we demonstrate a protocol that tolerates noise rates
up to . Hence, adaptivity circumvents an impossibility result of on
the fraction of tolerable noise (Braverman and Rao, 2014).Comment: Content is similar to previous version yet with an improved
presentatio
General Strong Polarization
Arikan's exciting discovery of polar codes has provided an altogether new way
to efficiently achieve Shannon capacity. Given a (constant-sized) invertible
matrix , a family of polar codes can be associated with this matrix and its
ability to approach capacity follows from the {\em polarization} of an
associated -bounded martingale, namely its convergence in the limit to
either or . Arikan showed polarization of the martingale associated with
the matrix to get
capacity achieving codes. His analysis was later extended to all matrices
that satisfy an obvious necessary condition for polarization.
While Arikan's theorem does not guarantee that the codes achieve capacity at
small blocklengths, it turns out that a "strong" analysis of the polarization
of the underlying martingale would lead to such constructions. Indeed for the
martingale associated with such a strong polarization was shown in two
independent works ([Guruswami and Xia, IEEE IT '15] and [Hassani et al., IEEE
IT '14]), resolving a major theoretical challenge of the efficient attainment
of Shannon capacity.
In this work we extend the result above to cover martingales associated with
all matrices that satisfy the necessary condition for (weak) polarization. In
addition to being vastly more general, our proofs of strong polarization are
also simpler and modular. Specifically, our result shows strong polarization
over all prime fields and leads to efficient capacity-achieving codes for
arbitrary symmetric memoryless channels. We show how to use our analyses to
achieve exponentially small error probabilities at lengths inverse polynomial
in the gap to capacity. Indeed we show that we can essentially match any error
probability with lengths that are only inverse polynomial in the gap to
capacity.Comment: 73 pages, 2 figures. The final version appeared in JACM. This paper
combines results presented in preliminary form at STOC 2018 and RANDOM 201
On the Feedback Capacity of the Fully Connected -User Interference Channel
The symmetric K user interference channel with fully connected topology is
considered, in which (a) each receiver suffers interference from all other
(K-1) transmitters, and (b) each transmitter has causal and noiseless feedback
from its respective receiver. The number of generalized degrees of freedom
(GDoF) is characterized in terms of \alpha, where the interference-to-noise
ratio (INR) is given by INR=SNR^\alpha. It is shown that the per-user GDoF of
this network is the same as that of the 2-user interference channel with
feedback, except for \alpha=1, for which existence of feedback does not help in
terms of GDoF. The coding scheme proposed for this network, termed cooperative
interference alignment, is based on two key ingredients, namely, interference
alignment and interference decoding. Moreover, an approximate characterization
is provided for the symmetric feedback capacity of the network, when the SNR
and INR are far apart from each other.Comment: 20 pages, 4 figures, to appear in IEEE Transactions on Information
Theor
Synchronization Strings: Codes for Insertions and Deletions Approaching the Singleton Bound
We introduce synchronization strings as a novel way of efficiently dealing
with synchronization errors, i.e., insertions and deletions. Synchronization
errors are strictly more general and much harder to deal with than commonly
considered half-errors, i.e., symbol corruptions and erasures. For every
, synchronization strings allow to index a sequence with an
size alphabet such that one can efficiently transform
synchronization errors into half-errors. This powerful new
technique has many applications. In this paper, we focus on designing insdel
codes, i.e., error correcting block codes (ECCs) for insertion deletion
channels.
While ECCs for both half-errors and synchronization errors have been
intensely studied, the later has largely resisted progress. Indeed, it took
until 1999 for the first insdel codes with constant rate, constant distance,
and constant alphabet size to be constructed by Schulman and Zuckerman. Insdel
codes for asymptotically large or small noise rates were given in 2016 by
Guruswami et al. but these codes are still polynomially far from the optimal
rate-distance tradeoff. This makes the understanding of insdel codes up to this
work equivalent to what was known for regular ECCs after Forney introduced
concatenated codes in his doctoral thesis 50 years ago.
A direct application of our synchronization strings based indexing method
gives a simple black-box construction which transforms any ECC into an equally
efficient insdel code with a slightly larger alphabet size. This instantly
transfers much of the highly developed understanding for regular ECCs over
large constant alphabets into the realm of insdel codes. Most notably, we
obtain efficient insdel codes which get arbitrarily close to the optimal
rate-distance tradeoff given by the Singleton bound for the complete noise
spectrum
EXIT-chart aided code design for symbol-based entanglement-assisted classical communication over quantum channels
Quantum-based transmission is an attractive solution conceived for achieving absolute security. In this quest, we have conceived an EXtrinsic Information Transfer (EXIT) chart aided channel code design for symbol-based entanglement-assisted classical communication over quantum depolarizing channels. Our proposed concatenated code design incorporates a Convolutional Code (CC), a symbol-based Unity Rate Code (URC) and a soft-decision aided 2-qubit Superdense Code (2SD), which is hence referred to as a CC-URC-2SD arrangement. We have optimized our design with the aid of non-binary EXIT charts. Our proposed design operates within 1 dB of the achievable capacity, providing attractive performance gains over its bit-based counterpart. Quantitatively, the bit-based scheme requires 60% more iterations than our symbol-based scheme for the sake of achieving perfect decoding convergence. Furthermore, we demonstrate that the decoding complexity can be reduced by using memory-2 and memory-3 convolutional codes, while still outperforming the bit-based approach<br/
Protecting the Future of Information: LOCO Coding With Error Detection for DNA Data Storage
DNA strands serve as a storage medium for -ary data over the alphabet
. DNA data storage promises formidable information density,
long-term durability, and ease of replicability. However, information in this
intriguing storage technology might be corrupted. Experiments have revealed
that DNA sequences with long homopolymers and/or with low -content are
notably more subject to errors upon storage.
This paper investigates the utilization of the recently-introduced method for
designing lexicographically-ordered constrained (LOCO) codes in DNA data
storage. This paper introduces DNA LOCO (D-LOCO) codes, over the alphabet
with limited runs of identical symbols. These codes come with an
encoding-decoding rule we derive, which provides affordable encoding-decoding
algorithms. In terms of storage overhead, the proposed encoding-decoding
algorithms outperform those in the existing literature. Our algorithms are
readily reconfigurable. D-LOCO codes are intrinsically balanced, which allows
us to achieve balancing over the entire DNA strand with minimal rate penalty.
Moreover, we propose four schemes to bridge consecutive codewords, three of
which guarantee single substitution error detection per codeword. We examine
the probability of undetecting errors. We also show that D-LOCO codes are
capacity-achieving and that they offer remarkably high rates at moderate
lengths.Comment: 14 pages (double column), 3 figures, submitted to the IEEE
Transactions on Molecular, Biological and Multi-scale Communications (TMBMC
Single-cell and multi-cell performance analysis of OFDM index modulation
This study addresses the achievable rate of single cell and sum rate of multi-cell orthogonal frequency division multiplexing (OFDM) index modulation (IM). The single-cell achievable rate of OFDM-IM with Gaussian input is calculated using a multi-ary symmetric channel. Then, the cumulative distribution function of multi-cell OFDM-IM is investigated by stochastic geometry. Furthermore, it is proved in this study that the probability density function of noise plus inter-cell interference in multicell OFDM-IM with quadrature-amplitude modulation follows a mixture of Gaussians (MoGs) distribution. Next, parameters of the MoG distribution are estimated using a simplified expectation maximisation algorithm. Upper bound of sum rates of multi-cell OFDM-IM is derived. Furthermore, analytic and simulated results are compared and discussed
Applications of Derandomization Theory in Coding
Randomized techniques play a fundamental role in theoretical computer science
and discrete mathematics, in particular for the design of efficient algorithms
and construction of combinatorial objects. The basic goal in derandomization
theory is to eliminate or reduce the need for randomness in such randomized
constructions. In this thesis, we explore some applications of the fundamental
notions in derandomization theory to problems outside the core of theoretical
computer science, and in particular, certain problems related to coding theory.
First, we consider the wiretap channel problem which involves a communication
system in which an intruder can eavesdrop a limited portion of the
transmissions, and construct efficient and information-theoretically optimal
communication protocols for this model. Then we consider the combinatorial
group testing problem. In this classical problem, one aims to determine a set
of defective items within a large population by asking a number of queries,
where each query reveals whether a defective item is present within a specified
group of items. We use randomness condensers to explicitly construct optimal,
or nearly optimal, group testing schemes for a setting where the query outcomes
can be highly unreliable, as well as the threshold model where a query returns
positive if the number of defectives pass a certain threshold. Finally, we
design ensembles of error-correcting codes that achieve the
information-theoretic capacity of a large class of communication channels, and
then use the obtained ensembles for construction of explicit capacity achieving
codes.
[This is a shortened version of the actual abstract in the thesis.]Comment: EPFL Phd Thesi
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