Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation

We present a continuous-variable quantum key distribution protocol combining a discrete modulation and reverse reconciliation. This protocol is proven unconditionally secure and allows the distribution of secret keys over long distances, thanks to a reverse reconciliation scheme efficient at very low signal-to-noise ratio.Comment: 4 pages, 2 figure

Belief propagation algorithm for computing correlation functions in finite-temperature quantum many-body systems on loopy graphs

Belief propagation -- a powerful heuristic method to solve inference problems involving a large number of random variables -- was recently generalized to quantum theory. Like its classical counterpart, this algorithm is exact on trees when the appropriate independence conditions are met and is expected to provide reliable approximations when operated on loopy graphs. In this paper, we benchmark the performances of loopy quantum belief propagation (QBP) in the context of finite-tempereture quantum many-body physics. Our results indicate that QBP provides reliable estimates of the high-temperature correlation function when the typical loop size in the graph is large. As such, it is suitable e.g. for the study of quantum spin glasses on Bethe lattices and the decoding of sparse quantum error correction codes.Comment: 5 pages, 4 figure

An efficient CDMA decoder for correlated information sources

We consider the detection of correlated information sources in the ubiquitous Code-Division Multiple-Access (CDMA) scheme. We propose a message-passing based scheme for detecting correlated sources directly, with no need for source coding. The detection is done simultaneously over a block of transmitted binary symbols (word). Simulation results are provided demonstrating a substantial improvement in bit-error-rate in comparison with the unmodified detector and the alternative of source compression. The robustness of the error-performance improvement is shown under practical model settings, including wrong estimation of the generating Markov transition matrix and finite-length spreading codes.Comment: 11 page

Statistical mechanics of error exponents for error-correcting codes

Error exponents characterize the exponential decay, when increasing message length, of the probability of error of many error-correcting codes. To tackle the long standing problem of computing them exactly, we introduce a general, thermodynamic, formalism that we illustrate with maximum-likelihood decoding of low-density parity-check (LDPC) codes on the binary erasure channel (BEC) and the binary symmetric channel (BSC). In this formalism, we apply the cavity method for large deviations to derive expressions for both the average and typical error exponents, which differ by the procedure used to select the codes from specified ensembles. When decreasing the noise intensity, we find that two phase transitions take place, at two different levels: a glass to ferromagnetic transition in the space of codewords, and a paramagnetic to glass transition in the space of codes.Comment: 32 pages, 13 figure

Finite size effects and error-free communication in Gaussian channels

The efficacy of a specially constructed Gallager-type error-correcting code to communication in a Gaussian channel is being examined. The construction is based on the introduction of complex matrices, used in both encoding and decoding, which comprise sub-matrices of cascading connection values. The finite size effects are estimated for comparing the results to the bounds set by Shannon. The critical noise level achieved for certain code-rates and infinitely large systems nearly saturates the bounds set by Shannon even when the connectivity used is low

Towards Quantum Belief Propagation for LDPC Decoding in Wireless Networks

We present Quantum Belief Propagation (QBP), a Quantum Annealing (QA) based decoder design for Low Density Parity Check (LDPC) error control codes, which have found many useful applications in Wi-Fi, satellite communications, mobile cellular systems, and data storage systems. QBP reduces the LDPC decoding to a discrete optimization problem, then embeds that reduced design onto quantum annealing hardware. QBP's embedding design can support LDPC codes of block length up to 420 bits on real state-of-the-art QA hardware with 2,048 qubits. We evaluate performance on real quantum annealer hardware, performing sensitivity analyses on a variety of parameter settings. Our design achieves a bit error rate of $10^{-8}$ in 20 $\mu$s and a 1,500 byte frame error rate of $10^{-6}$ in 50 $\mu$s at SNR 9 dB over a Gaussian noise wireless channel. Further experiments measure performance over real-world wireless channels, requiring 30 $\mu$s to achieve a 1,500 byte 99.99$\%$ frame delivery rate at SNR 15-20 dB. QBP achieves a performance improvement over an FPGA based soft belief propagation LDPC decoder, by reaching a bit error rate of $10^{-8}$ and a frame error rate of $10^{-6}$ at an SNR 2.5--3.5 dB lower. In terms of limitations, QBP currently cannot realize practical protocol-sized ($\textit{e.g.,}$ Wi-Fi, WiMax) LDPC codes on current QA processors. Our further studies in this work present future cost, throughput, and QA hardware trend considerations

Statistical Physics of Irregular Low-Density Parity-Check Codes

Low-density parity-check codes with irregular constructions have been recently shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of simple irregular codes. We use the replica method to find a phase transition which coincides with Shannon's coding bound when appropriate parameters are chosen. The decoding by belief propagation is also studied using statistical physics arguments; the theoretical solutions obtained are in good agreement with simulations. We compare the performance of irregular with that of regular codes and discuss the factors that contribute to the improvement in performance.Comment: 20 pages, 9 figures, revised version submitted to JP

Error-correcting codes that nearly saturate Shannon's bound

Gallager-type error-correcting codes that nearly saturate Shannon's bound are constructed using insight gained from mapping the problem onto that of an Ising spin system. The performance of the suggested codes is evaluated for different code rates in both finite and infinite message length

Gain-of-Function Mutation in Filamin A Potentiates Platelet Integrin αβ Activation

OBJECTIVE: Dominant mutations of the X-linked filamin A () gene are responsible for filaminopathies A, which are rare disorders including brain periventricular nodular heterotopia, congenital intestinal pseudo-obstruction, cardiac valves or skeleton malformations, and often macrothrombocytopenia. APPROACH AND RESULTS: We studied a male patient with periventricular nodular heterotopia and congenital intestinal pseudo-obstruction, his unique X-linked allele carrying a stop codon mutation resulting in a 100-amino acid-long FLNa C-terminal extension (NP_001447.2: ). Platelet counts were normal, with few enlarged platelets. FLNa was detectable in all platelets but at 30% of control levels. Surprisingly, all platelet functions were significantly upregulated, including platelet aggregation and secretion, as induced by ADP, collagen, or von Willebrand factor in the presence of ristocetin, as well as thrombus formation in blood flow on a collagen or on a von Willebrand factor matrix. Most importantly, patient platelets stimulated with ADP exhibited a marked increase in αβ integrin activation and a parallel increase in talin recruitment to β, contrasting with normal Rap1 activation. These results are consistent with the mutant FLNa affecting the last step of αβ activation. Overexpression of mutant FLNa in the HEL megakaryocytic cell line correlated with an increase (compared with wild-type FLNa) in PMA-induced fibrinogen binding to and in talin and kindlin-3 recruitment by αβ. CONCLUSIONS: Altogether, our results are consistent with a less binding of mutant FLNa to β and the facilitated recruitment of talin by β on platelet stimulation, explaining the increased αβ activation and the ensuing gain-of-platelet functions

Determinants of the voltage dependence of G protein modulation within calcium channel β subunits

CaVβ subunits of voltage-gated calcium channels contain two conserved domains, a src-homology-3 (SH3) domain and a guanylate kinase-like (GK) domain with an intervening HOOK domain. We have shown in a previous study that, although Gβγ-mediated inhibitory modulation of CaV2.2 channels did not require the interaction of a CaVβ subunit with the CaVα1 subunit, when such interaction was prevented by a mutation in the α1 subunit, G protein modulation could not be removed by a large depolarization and showed voltage-independent properties (Leroy et al., J Neurosci 25:6984–6996, 2005). In this study, we have investigated the ability of mutant and truncated CaVβ subunits to support voltage-dependent G protein modulation in order to determine the minimal domain of the CaVβ subunit that is required for this process. We have coexpressed the CaVβ subunit constructs with CaV2.2 and α2δ-2, studied modulation by the activation of the dopamine D2 receptor, and also examined basal tonic modulation. Our main finding is that the CaVβ subunit GK domains, from either β1b or β2, are sufficient to restore voltage dependence to G protein modulation. We also found that the removal of the variable HOOK region from β2a promotes tonic voltage-dependent G protein modulation. We propose that the absence of the HOOK region enhances Gβγ binding affinity, leading to greater tonic modulation by basal levels of Gβγ. This tonic modulation requires the presence of an SH3 domain, as tonic modulation is not supported by any of the CaVβ subunit GK domains alone