arXiv subjects

Ido Kanter

Publications and source records attributed to Ido Kanter.

At least 91 records · Page 5Linked to original sources

arXiv2004

An Efficient MN-Algorithm for Joint Source-Channel Coding

Belief Propagation (BP) decoding of LDPC codes is extended to the case of Joint Source-Channel coding. The uncompressed source is treated as a Markov process, characterized by a transition matrix, T, which is utilized as side information for the Joint scheme. The method is based on the ability to calculate a Dynamical Block Prior (DBP), for each decoded symbol separately, and re-estimate this prior after every iteration of the BP decoder. We demonstrate the implementation of this method using MacKay and Neel's LDPC algorithm over GF(q), and present simulation results indicating that the proposed scheme is comparable with Separation scheme, even when advanced compression algorithms (such as AC, PPM) are used. The extension to 2D (and higher) arrays of symbols is straight-forward. The possibility of using the proposed scheme without side information is briefly sketched.

cond-mat.dis-nn↗

arXiv2004

An Efficient Joint Source-Channel Decoder with Dynamical Block Priors

An efficient joint source-channel (s/c) decoder based on the side information of the source and on the MN-Gallager algorithm over Galois fields is presented. The dynamical block priors (DBP) are derived either from a statistical mechanical approach via calculation of the entropy for the correlated sequences, or from the Markovian transition matrix. The Markovian joint s/c decoder has many advantages over the statistical mechanical approach. In particular, there is no need for the construction and the diagonalization of a qXq matrix and for a solution to saddle point equations in q dimensions. Using parametric estimation, an efficient joint s/c decoder with the lack of side information is discussed. Besides the variant joint s/c decoders presented, we also show that the available sets of autocorrelations consist of a convex volume, and its structure can be found using the Simplex algorithm.

cond-mat.dis-nn↗

arXiv2004

Neural cryptography with feedback

Neural cryptography is based on a competition between attractive and repulsive stochastic forces. A feedback mechanism is added to neural cryptography which increases the repulsive forces. Using numerical simulations and an analytic approach, the probability of a successful attack is calculated for different model parameters. Scaling laws are derived which show that feedback improves the security of the system. In addition, a network with feedback generates a pseudorandom bit sequence which can be used to encrypt and decrypt a secret message.

cond-mat.dis-nn↗

arXiv2004

Is a multiple excitation of a single atom equivalent to a single excitation of an ensemble of atoms?

Recent technological advances have enabled to isolate, control and measure the properties of a single atom, leading to the possibility to perform statistics on the behavior of single quantum systems. These experiments have enabled to check a question which was out of reach previously: Is the statistics of a repeatedly excitation of an atom N times equivalent to a single excitation of an ensemble of N atoms? We present a new method to analyze quantum measurements which leads to the postulation that the answer is most probably no. We discuss the merits of the analysis and its conclusion.

physics.atom-ph↗

arXiv2004

Utilizing hidden Markov processes as a new tool for experimental physics

A hidden Markov process is a well known concept in information theory and is used for a vast range of applications such as speech recognition and error correction. We bridge between two disciplines, experimental physics and advanced algorithms, and propose to use a physically oriented hidden Markov process as a new tool for analyzing experimental data. This tool enables one to extract valuable information on physical parameters of complex systems. We demonstrate the usefulness of this technique on low dimensional electronic systems which exhibit time dependent resistance noise. This method is expected to become a standard technique in experimental physics.

cond-mat.mes-hall↗

arXiv2003

An efficient joint source-channel coding for a D-dimensional array

An efficient joint source-channel (S/C) decoder based on the side information of the source and on the MN-Gallager Code over Galois fields, $q$, is presented. The dynamical posterior probabilities are derived either from the statistical mechanical approach for calculation of the entropy for the correlated sequences, or by the Markovian joint S/C algorithm. The Markovian joint S/C decoder has many advantages over the statistical mechanical approach, among them: (a) there is no need for the construction and the diagonalization of a $q \times q$ matrix and for a solution to saddle point equations in $q$ dimensions; (b) a generalization to a joint S/C coding of an array of two-dimensional bits (or higher dimensions) is achievable; (c) using parametric estimation, an efficient joint S/C decoder with the lack of side information is discussed. Besides the variant joint S/C decoders presented, we also show that the available sets of autocorrelations consist of a convex volume, and its structure can be found using the Simplex algorithm.

cond-mat.stat-mech↗

arXiv2003

Statistical mechanical aspects of joint source-channel coding

An MN-Gallager Code over Galois fields, $q$, based on the Dynamical Block Posterior probabilities (DBP) for messages with a given set of autocorrelations is presented with the following main results: (a) for a binary symmetric channel the threshold, $f_c$, is extrapolated for infinite messages using the scaling relation for the median convergence time, $t_{med} \propto 1/(f_c-f)$; (b) a degradation in the threshold is observed as the correlations are enhanced; (c) for a given set of autocorrelations the performance is enhanced as $q$ is increased; (d) the efficiency of the DBP joint source-channel coding is slightly better than the standard gzip compression method; (e) for a given entropy, the performance of the DBP algorithm is a function of the decay of the correlation function over large distances.

cond-mat.stat-mech↗

arXiv2003

Public channel cryptography by synchronization of neural networks and chaotic maps

Two different kinds of synchronization have been applied to cryptography: Synchronization of chaotic maps by one common external signal and synchronization of neural networks by mutual learning. By combining these two mechanisms, where the external signal to the chaotic maps is synchronized by the nets, we construct a hybrid network which allows a secure generation of secret encryption keys over a public channel. The security with respect to attacks, recently proposed by Shamir et al, is increased by chaotic synchronization.

cond-mat.stat-mech↗

arXiv2003

Communication near the channel capacity with an absence of compression: Statistical Mechanical Approach

The generalization of Shannon's theory to include messages with given autocorrelations is presented. The analytical calculation of the channel capacity is based on the transfer matrix method of the effective 1D Hamiltonian. This bridge between statistical physics and information theory leads to efficient Low-Density Parity-Check Codes over Galois fields that nearly saturate the channel capacity. The novel idea of the decoder is the dynamical updating of the prior block probabilities which are derived from the transfer matrix solution and from the posterior probabilities of the neighboring blocks. Application and possible extensions are discussed, specifically the possibility of achieving the channel capacity without compression of the data.

cond-mat.stat-mech↗

arXiv2002

Mutual learning in a tree parity machine and its application to cryptography

Mutual learning of a pair of tree parity machines with continuous and discrete weight vectors is studied analytically. The analysis is based on a mapping procedure that maps the mutual learning in tree parity machines onto mutual learning in noisy perceptrons. The stationary solution of the mutual learning in the case of continuous tree parity machines depends on the learning rate where a phase transition from partial to full synchronization is observed. In the discrete case the learning process is based on a finite increment and a full synchronized state is achieved in a finite number of steps. The synchronization of discrete parity machines is introduced in order to construct an ephemeral key-exchange protocol. The dynamic learning of a third tree parity machine (an attacker) that tries to imitate one of the two machines while the two still update their weight vectors is also analyzed. In particular, the synchronization times of the naive attacker and the flipping attacker recently introduced in [1] are analyzed. All analytical results are found to be in good agreement with simulation results.

cond-mat.dis-nn↗

arXiv2002

Neural Cryptography

Two neural networks which are trained on their mutual output bits show a novel phenomenon: The networks synchronize to a state with identical time dependent weights. It is shown how synchronization by mutual learning can be applied to cryptography: secret key exchange over a public channel.

cond-mat.dis-nn↗

arXiv2002

A secure key-exchange protocol with an absence of injective functions

The security of neural cryptography is investigated. A key-exchange protocol over a public channel is studied where the parties exchanging secret messages use multilayer neural networks which are trained by their mutual output bits and synchronize to a time dependent secret key. The weights of the networks have integer values between $\pm L$. Recently an algorithm for an eavesdropper which could break the key was introduced by Shamir et al. [adi]. We show that the synchronization time increases with $L^2$ while the probability to find a successful attacker decreases exponentially with $L$. Hence for large $L$ we find a secure key-exchange protocol which depends neither on number theory nor on injective trapdoor functions used in conventional cryptography.

cond-mat.dis-nn↗

arXiv2002

Interacting neural networks and cryptography

Two neural networks which are trained on their mutual output bits are analysed using methods of statistical physics. The exact solution of the dynamics of the two weight vectors shows a novel phenomenon: The networks synchronize to a state with identical time dependent weights. Extending the models to multilayer networks with discrete weights, it is shown how synchronization by mutual learning can be applied to secret key exchange over a public channel.

cond-mat.dis-nn↗

arXiv2002

Learning and predicting time series by neural networks

Artificial neural networks which are trained on a time series are supposed to achieve two abilities: firstly to predict the series many time steps ahead and secondly to learn the rule which has produced the series. It is shown that prediction and learning are not necessarily related to each other. Chaotic sequences can be learned but not predicted while quasiperiodic sequences can be well predicted but not learned.

cond-mat.dis-nn↗

arXiv2002

Cryptography based on neural networks - analytical results

Mutual learning process between two parity feed-forward networks with discrete and continuous weights is studied analytically, and we find that the number of steps required to achieve full synchronization between the two networks in the case of discrete weights is finite. The synchronization process is shown to be non-self-averaging and the analytical solution is based on random auxiliary variables. The learning time of an attacker that is trying to imitate one of the networks is examined analytically and is found to be much longer than the synchronization time. Analytical results are found to be in agreement with simulations.

cond-mat.stat-mech↗

arXiv2001

Generation of unpredictable time series by a Neural Network

A perceptron that learns the opposite of its own output is used to generate a time series. We analyse properties of the weight vector and the generated sequence, like the cycle length and the probability distribution of generated sequences. A remarkable suppression of the autocorrelation function is explained, and connections to the Bernasconi model are discussed. If a continuous transfer function is used, the system displays chaotic and intermittent behaviour, with the product of the learning rate and amplification as a control parameter.

cond-mat.dis-nn↗

arXiv2001

Multilayer neural networks with extensively many hidden units

The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is performed by general symmetric Boolean functions whereas the hidden layer is connected to the output by either discrete or continuous couplings. Introducing an overlap in the space of Boolean functions as order parameter the storage capacity if found to scale with the logarithm of the number of implementable Boolean functions. The generalization behaviour is smooth for continuous couplings and shows a discontinuous transition to perfect generalization for discrete ones.

cond-mat.stat-mech↗

arXiv2001

Low autocorrelated multi-phase sequences

The interplay between the ground state energy of the generalized Bernasconi model to multi-phase, and the minimal value of the maximal autocorrelation function, $C_{max}=\max_K{|C_K|}$, $K=1,..N-1$, is examined analytically and the main results are: (a) The minimal value of $\min_N{C_{max}}$ is $0.435\sqrt{N}$ significantly smaller than the typical value for random sequences $O(\sqrt{\log{N}}\sqrt{N})$. (b) $\min_N{C_{max}}$ over all sequences of length N is obtained in an energy which is about 30% above the ground-state energy of the generalized Bernasconi model, independent of the number of phases m. (c) The maximal merit factor $F_{max}$ grows linearly with m. (d) For a given N, $\min_N{C_{max}}\sim\sqrt{N/m}$ indicating that for m=N, $\min_N{C_{max}}=1$, i.e. a Barker code exits. The analytical results are confirmed by simulations.

cond-mat.stat-mech↗