134 research outputs found
Capacity-achieving ensembles for the binary erasure channel with bounded complexity
We present two sequences of ensembles of non-systematic irregular
repeat-accumulate codes which asymptotically (as their block length tends to
infinity) achieve capacity on the binary erasure channel (BEC) with bounded
complexity per information bit. This is in contrast to all previous
constructions of capacity-achieving sequences of ensembles whose complexity
grows at least like the log of the inverse of the gap (in rate) to capacity.
The new bounded complexity result is achieved by puncturing bits, and allowing
in this way a sufficient number of state nodes in the Tanner graph representing
the codes. We also derive an information-theoretic lower bound on the decoding
complexity of randomly punctured codes on graphs. The bound holds for every
memoryless binary-input output-symmetric channel and is refined for the BEC.Comment: 47 pages, 9 figures. Submitted to IEEE Transactions on Information
Theor
A Generalization of the Finite-Length Scaling Approach Beyond the BEC
We want to extend the approximation of the error probability via a scaling approach from the BEC to general binary-input memoryless output-symmetric (BMS) channels. In particular, we consider such scaling laws for regular LDPC ensembles and message-passing (MP) decoders with a finite number of messages. We first show how to re-derive the scaling law for transmission over the BEC using an “EXIT-like” curve instead of the density evolution curve of the peeling decoder. The advantage of the new derivation is that the new expression of the scaling parameter α only contains quantities that can be meaningfully interpreted also for general message-passing algorithms. In particular, this expression only depends on the curvature of the EXIT-like curve as well as the variance of the messages, both taken at the critical channel parameter. We discuss how to compute these quantities for general MP algorithms and we evaluate the expressions for the specific cases of the Gallager algorithm A as well as the Decoder with Erasures and compare the resulting predictions on the error probability with simulation results
Geometry of entangled states, Bloch spheres and Hopf fibrations
We discuss a generalization to 2 qubits of the standard Bloch sphere
representation for a single qubit, in the framework of Hopf fibrations of high
dimensional spheres by lower dimensional spheres. The single qubit Hilbert
space is the 3-dimensional sphere S3. The S2 base space of a suitably oriented
S3 Hopf fibration is nothing but the Bloch sphere, while the circular fibres
represent the qubit overall phase degree of freedom. For the two qubits case,
the Hilbert space is a 7-dimensional sphere S7, which also allows for a Hopf
fibration, with S3 fibres and a S4 base. A main striking result is that
suitably oriented S7 Hopf fibrations are entanglement sensitive. The relation
with the standard Schmidt decomposition is also discussedComment: submitted to J. Phys.
Geometrical organization of solutions to random linear Boolean equations
The random XORSAT problem deals with large random linear systems of Boolean
variables. The difficulty of such problems is controlled by the ratio of number
of equations to number of variables. It is known that in some range of values
of this parameter, the space of solutions breaks into many disconnected
clusters. Here we study precisely the corresponding geometrical organization.
In particular, the distribution of distances between these clusters is computed
by the cavity method. This allows to study the `x-satisfiability' threshold,
the critical density of equations where there exist two solutions at a given
distance.Comment: 20 page
Achievable rates for the Gaussian quantum channel
We study the properties of quantum stabilizer codes that embed a
finite-dimensional protected code space in an infinite-dimensional Hilbert
space. The stabilizer group of such a code is associated with a symplectically
integral lattice in the phase space of 2N canonical variables. From the
existence of symplectically integral lattices with suitable properties, we
infer a lower bound on the quantum capacity of the Gaussian quantum channel
that matches the one-shot coherent information optimized over Gaussian input
states.Comment: 12 pages, 4 eps figures, REVTe
Guest Editorial Recent Advances in Capacity Approaching Codes
[No abstract available
HDAC inhibitor-dependent transcriptome and memory reinstatement in cognitive decline models.
Aging and increased amyloid burden are major risk factors for cognitive diseases such as Alzheimer's disease (AD). Effective therapies for these diseases are lacking. Here, we evaluated mouse models of age-associated memory impairment and amyloid deposition to study transcriptome and cell type-specific epigenome plasticity in the brain and peripheral organs. We determined that aging and amyloid pathology are associated with inflammation and impaired synaptic function in the hippocampal CA1 region as the result of epigenetic-dependent alterations in gene expression. In both amyloid and aging models, inflammation was associated with increased gene expression linked to a subset of transcription factors, while plasticity gene deregulation was differentially mediated. Amyloid pathology impaired histone acetylation and decreased expression of plasticity genes, while aging altered H4K12 acetylation-linked differential splicing at the intron-exon junction in neurons, but not nonneuronal cells. Furthermore, oral administration of the clinically approved histone deacetylase inhibitor vorinostat not only restored spatial memory, but also exerted antiinflammatory action and reinstated epigenetic balance and transcriptional homeostasis at the level of gene expression and exon usage. This study provides a systems-level investigation of transcriptome plasticity in the hippocampal CA1 region in aging and AD models and suggests that histone deacetylase inhibitors should be further explored as a cost-effective therapeutic strategy against age-associated cognitive decline
Device-Independent Quantum Key Distribution
Cryptographic key exchange protocols traditionally rely on computational
conjectures such as the hardness of prime factorisation to provide security
against eavesdropping attacks. Remarkably, quantum key distribution protocols
like the one proposed by Bennett and Brassard provide information-theoretic
security against such attacks, a much stronger form of security unreachable by
classical means. However, quantum protocols realised so far are subject to a
new class of attacks exploiting implementation defects in the physical devices
involved, as demonstrated in numerous ingenious experiments. Following the
pioneering work of Ekert proposing the use of entanglement to bound an
adversary's information from Bell's theorem, we present here the experimental
realisation of a complete quantum key distribution protocol immune to these
vulnerabilities. We achieve this by combining theoretical developments on
finite-statistics analysis, error correction, and privacy amplification, with
an event-ready scheme enabling the rapid generation of high-fidelity
entanglement between two trapped-ion qubits connected by an optical fibre link.
The secrecy of our key is guaranteed device-independently: it is based on the
validity of quantum theory, and certified by measurement statistics observed
during the experiment. Our result shows that provably secure cryptography with
real-world devices is possible, and paves the way for further quantum
information applications based on the device-independence principle.Comment: 5+1 pages in main text and methods with 4 figures and 1 table; 37
pages of supplementary materia
Threshold Saturation in Spatially Coupled Constraint Satisfaction Problems
We consider chains of random constraint satisfaction models that are
spatially coupled across a finite window along the chain direction. We
investigate their phase diagram at zero temperature using the survey
propagation formalism and the interpolation method. We prove that the SAT-UNSAT
phase transition threshold of an infinite chain is identical to the one of the
individual standard model, and is therefore not affected by spatial coupling.
We compute the survey propagation complexity using population dynamics as well
as large degree approximations, and determine the survey propagation threshold.
We find that a clustering phase survives coupling. However, as one increases
the range of the coupling window, the survey propagation threshold increases
and saturates towards the phase transition threshold. We also briefly discuss
other aspects of the problem. Namely, the condensation threshold is not
affected by coupling, but the dynamic threshold displays saturation towards the
condensation one. All these features may provide a new avenue for obtaining
better provable algorithmic lower bounds on phase transition thresholds of the
individual standard model
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