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Misha Stepanov

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Julie T Daniels

University College London

University College London

Plymouth University

Joseph Shalhoub

Imperial College London

José Francisco Pessanha

UERJ - Universidade do Estado do Rio de Janeiro / Rio de Janeiro State University

Adebayo D Agunbiade

Olabisi Onabanjo University, Ago-Iwoye, Nigeria

Yogendra Chaubey

Concordia University (Canada)

Nikos Mantzakouras

National & Kapodistrian University of Athens

Yildiz Technical University

Elisa Hill-yardin

University of Melbourne

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Papers by Misha Stepanov

Statistics of turbulence-induced fluctuations of particles concentration

by G. Falkovich and Misha Stepanov

Resonant peak in detuning curve of ionic anti-Stokes Raman laser

Conference Digest. 2000 International Quantum Electronics Conference (Cat. No.00TH8504), 2000

Summary form only given. A CW anti-Stokes Raman laser (ASRL) in ionic system enables up-conversio... more Summary form only given. A CW anti-Stokes Raman laser (ASRL) in ionic system enables up-conversion of high efficiency and large frequency shift. In a Λ-system, the pump radiation of frequency ωp is converted into a Raman laser output of frequency ω in the process of resonant interaction with ionic levels. Various schemes in ArII system with a metastable start level

Exact and efficient algorithm to discover extreme stochastic events in wind generation over transmission Power Grids

IEEE Conference on Decision and Control and European Control Conference, 2011

In this manuscript we continue the thread of [M. Chertkov, F. Pan, M. Stepanov, Predicting Failur... more

Instanton analysis of Low-Density Parity-Check codes in the error-floor regime

2006 IEEE International Symposium on Information Theory, 2006

In this paper we develop instanton method introduced in [1], [2], [3] to analyze quantitatively p... more In this paper we develop instanton method introduced in [1], [2], [3] to analyze quantitatively performance of Low-Density-Parity-Check (LDPC) codes decoded iteratively in the so-called error-floor regime. We discuss statistical properties of the numerical instanton-amoeba scheme focusing on detailed analysis and comparison of two regular LDPC codes: Tanner's (155, 64, 20) and Margulis' (672, 336, 16) codes. In the regime of moderate values of the signal-to-noise ratio we critically compare results of the instanton-amoeba evaluations against the standard Monte-Carlo calculations of the Frame-Error-Rate.

Growth of density inhomogeneities in a flow of wave turbulence

Physical review letters, Jan 18, 2004

We consider the flow being a superposition of random waves and describe the evolution of the spec... more We consider the flow being a superposition of random waves and describe the evolution of the spectrum of the passive scalar in the leading (fourth) order with respect to the wave amplitudes. We find that wave turbulence can produce an exponential growth of the passive scalar fluctuations when either both solenoidal and potential components are present in the flow or there are potential waves with the same frequencies but different wave numbers.

Statistics of interacting optical solitons

Physical review. E, Statistical, nonlinear, and soft matter physics, 2001

We examine statistics of two interacting optical solitons and describe timing jitter caused by sp... more We examine statistics of two interacting optical solitons and describe timing jitter caused by spontaneous emission noise and enhanced by pulse interaction. Dynamics of phase difference is shown to be of crucial importance in determining the probability distribution function (PDF) of the distance between solitons. We find analytically the non-Gaussian tail of the PDF to be exponential. The propagation distance that corresponds to a given bit-error rate is described as a function of system parameters (filtering and noise level), initial distance, and initial phase difference between solitons. We find the interval of parameters where a larger propagation distance can be achieved for higher density of information.

Polytope of correct (linear programming) decoding and low-weight pseudo-codewords

2011 IEEE International Symposium on Information Theory Proceedings, 2011

We analyze Linear Programming (LP) decoding of graphical binary codes operating over soft-output,... more We analyze Linear Programming (LP) decoding of graphical binary codes operating over soft-output, symmetric and log-concave channels. We show that the error-surface, separating domain of the correct decoding from domain of the erroneous decoding, is a polytope. We formulate the problem of finding the lowest-weight pseudo-codeword as a nonconvex optimization (maximization of a convex function) over a polytope, with the cost function defined by the channel and the polytope defined by the structure of the code. This formulation suggests new heuristics for finding the lowest weight pseudocodewords, which is advantageous in comparison with the one discussed previously, in particular because of being provably monotonic and also resulting in more frequent discoveries of pseudo-codewords with the lowest weights. The algorithm performance is tested on the example of the Tanner [155, 64, code over the Additive White Gaussian Noise (AWGN) channel.

Searching for low weight pseudo-codewords

2007 Information Theory and Applications Workshop, 2007

Photoexcited wavepacket scattering on conical intersections: Semiclassical expansion

by Misha Stepanov and Vladimir Chernyak

Notes about Passive Scalar in Large-Scale Velocity Field

Predicting failures in power grids

Detuning characteristics of ionic anti-Stokes Raman laser

Continuous-wave generation is demonstrated of the anti- Stokes Raman laser in new (Alpha) scheme ... more Continuous-wave generation is demonstrated of the anti- Stokes Raman laser in new (Alpha) scheme ArII 3d'2G9/2 yields 4p'2F7/2 yields 4s'2D5/2 with long- lived start and final levels. Red pump radiation with wavelength (lambda) p equals 611 nm from a dye laser that excites transition 3d'2G9/2 yields 4p'2F7/2 is converted into the blue radiation at (lambda) equals 461 nm (4p'2F7/2 yields

Pseudo-codeword Landscape

2007 IEEE International Symposium on Information Theory, 2007

We discuss the performance of Low-Density-Parity-Check (LDPC) codes decoded by means of Linear Pr... more We discuss the performance of Low-Density-Parity-Check (LDPC) codes decoded by means of Linear Programming (LP) at moderate and large Signal-to-Noise-Ratios (SNR). Utilizing a combination of the previously introduced pseudocodeword-search method and a new "dendro" trick, which allows us to reduce the complexity of the LP decoding, we analyze the dependence of the Frame-Error-Rate (FER) on the SNR. Under Maximum-A-Posteriori (MAP) decoding the dendro-code, having only checks with connectivity degree three, performs identically to its original code with high-connectivity checks. For a number of popular LDPC codes performing over the Additive-White-Gaussian-Noise (AWGN) channel we found that either an errorfloor sets at a relatively low SNR, or otherwise a transient asymptote, characterized by a faster decay of FER with the SNR increase, precedes the error-floor asymptote. We explain these regimes in terms of the pseudo-codeword spectra of the codes.

Analysis of error floors of LDPC codes under LP decoding over the BSC

2009 IEEE International Symposium on Information Theory, 2009

... Analysis of Error Floors of LDPC Codes under LP Decoding over the BSC Shashi Kiran Chilappaga... more

Instanton method of post-error-correction analytical evaluation

by Misha Stepanov and Vladimir Chernyak

Manufacturing Engineer, 2004

We present a theoretical tool for evalu a t i o n of the error codes' p e r f o r m a n c e on gr... more We present a theoretical tool for evalu a t i o n of the error codes' p e r f o r m a n c e on graphs. T h e m e t h o d is k n o w n u n d e r the n a m e of instanton calculus and is c o m m o n i n theoretical physics. We introduce the i n s t a n t o n calculus for linear block codes, a n d give a closed f o r m expression for t h e b i t error rate for a class of codes whose graphical m o d e l is a p p r o x i m a t e d locally by a tree.

Diagnosis of Weaknesses in Modern Error Correction Codes: A Physics Approach

by Misha Stepanov and Vladimir Chernyak

Physical Review Letters, 2005

One of the main obstacles to the wider use of the modern error-correction codes is that, due to t... more One of the main obstacles to the wider use of the modern error-correction codes is that, due to the complex behavior of their decoding algorithms, no systematic method which would allow characterization of the bit-error-rate (BER) is known. This is especially true at the weak noise where many systems operate and where coding performance is difficult to estimate because of the diminishingly small number of errors. We show how the instanton method of physics allows one to solve the problem of BER analysis in the weak noise range by recasting it as a computationally tractable minimization problem.

Semiclassical Scattering on Conical Intersections

by Misha Stepanov and Vladimir Chernyak

Physical Review Letters, 2005

We apply a semiclassical approach to the scattering problem of a vibrational wave packet in the v... more We apply a semiclassical approach to the scattering problem of a vibrational wave packet in the vicinity of a conical intersection of electronic energy surfaces and derive analytical expressions for the scattering matrix. The latter are valid when the scattering length that scales as @ p is small and a wave packet passes through the scattering region with a constant velocity. The analytical results are in excellent agreement with numerical simulations for a realistic set of parameters.

Error Correction on a Tree: An Instanton Approach

by Misha Stepanov and Vladimir Chernyak

Physical Review Letters, 2004

We introduce a method that allows analytical or semianalytical estimating of the post-error corre... more We introduce a method that allows analytical or semianalytical estimating of the post-error correction bit error rate (BER) when a forward-error correction is utilized for transmitting information through a noisy channel. The generic method that applies to a variety of error-correction schemes in the regimes where the BER is low is illustrated using the example of a finite-size code approximated by a treelike structure. Exploring the statistical physics formulation of the problem we find that the BER decreases with the signal-to-noise ratio nonuniformly, i.e., crossing over through a sequence of phases. The higher the signal-to-noise ratio the lower the symmetry of the phase dominating BER.

New bisoliton solutions in dispersion managed systems

Physica D: Nonlinear Phenomena, 2009

In this paper we propose a method which provides a full description of solitary wave solutions of... more In this paper we propose a method which provides a full description of solitary wave solutions of the Schrödinger equation with periodically varying dispersion. This method is based on analysis and polynomial deformation of the spectrum of an iterative map. Using this method we discover a new family of antisymmetric bisoliton solutions. In addition to the fact that these solutions are of interest for nonlinear fiber optics and the theory of nonlinear Schrödinger equations with periodic coefficients, they have potential applications for increasing of bit-rate in high speed optical fiber communications.

Role of interaction in causing errors in optical soliton transmission

Optics Letters, 2002

We consider two solitons propagating under a filter-control scheme and describe the timing jitter... more We consider two solitons propagating under a filter-control scheme and describe the timing jitter that is caused by spontaneous-emission noise and enhanced by attraction between solitons. We find the bit-error rate as a function of system parameters (filtering and noise level), timing, initial distance, and the phase difference between solitons.

Statistics of turbulence-induced fluctuations of particles concentration

by G. Falkovich and Misha Stepanov

Resonant peak in detuning curve of ionic anti-Stokes Raman laser

Conference Digest. 2000 International Quantum Electronics Conference (Cat. No.00TH8504), 2000

Summary form only given. A CW anti-Stokes Raman laser (ASRL) in ionic system enables up-conversio... more Summary form only given. A CW anti-Stokes Raman laser (ASRL) in ionic system enables up-conversion of high efficiency and large frequency shift. In a Λ-system, the pump radiation of frequency ωp is converted into a Raman laser output of frequency ω in the process of resonant interaction with ionic levels. Various schemes in ArII system with a metastable start level

Exact and efficient algorithm to discover extreme stochastic events in wind generation over transmission Power Grids

IEEE Conference on Decision and Control and European Control Conference, 2011

In this manuscript we continue the thread of [M. Chertkov, F. Pan, M. Stepanov, Predicting Failur... more

Instanton analysis of Low-Density Parity-Check codes in the error-floor regime

2006 IEEE International Symposium on Information Theory, 2006

In this paper we develop instanton method introduced in [1], [2], [3] to analyze quantitatively p... more In this paper we develop instanton method introduced in [1], [2], [3] to analyze quantitatively performance of Low-Density-Parity-Check (LDPC) codes decoded iteratively in the so-called error-floor regime. We discuss statistical properties of the numerical instanton-amoeba scheme focusing on detailed analysis and comparison of two regular LDPC codes: Tanner's (155, 64, 20) and Margulis' (672, 336, 16) codes. In the regime of moderate values of the signal-to-noise ratio we critically compare results of the instanton-amoeba evaluations against the standard Monte-Carlo calculations of the Frame-Error-Rate.

Growth of density inhomogeneities in a flow of wave turbulence

Physical review letters, Jan 18, 2004

We consider the flow being a superposition of random waves and describe the evolution of the spec... more We consider the flow being a superposition of random waves and describe the evolution of the spectrum of the passive scalar in the leading (fourth) order with respect to the wave amplitudes. We find that wave turbulence can produce an exponential growth of the passive scalar fluctuations when either both solenoidal and potential components are present in the flow or there are potential waves with the same frequencies but different wave numbers.

Statistics of interacting optical solitons

Physical review. E, Statistical, nonlinear, and soft matter physics, 2001

We examine statistics of two interacting optical solitons and describe timing jitter caused by sp... more We examine statistics of two interacting optical solitons and describe timing jitter caused by spontaneous emission noise and enhanced by pulse interaction. Dynamics of phase difference is shown to be of crucial importance in determining the probability distribution function (PDF) of the distance between solitons. We find analytically the non-Gaussian tail of the PDF to be exponential. The propagation distance that corresponds to a given bit-error rate is described as a function of system parameters (filtering and noise level), initial distance, and initial phase difference between solitons. We find the interval of parameters where a larger propagation distance can be achieved for higher density of information.

Polytope of correct (linear programming) decoding and low-weight pseudo-codewords

2011 IEEE International Symposium on Information Theory Proceedings, 2011

We analyze Linear Programming (LP) decoding of graphical binary codes operating over soft-output,... more We analyze Linear Programming (LP) decoding of graphical binary codes operating over soft-output, symmetric and log-concave channels. We show that the error-surface, separating domain of the correct decoding from domain of the erroneous decoding, is a polytope. We formulate the problem of finding the lowest-weight pseudo-codeword as a nonconvex optimization (maximization of a convex function) over a polytope, with the cost function defined by the channel and the polytope defined by the structure of the code. This formulation suggests new heuristics for finding the lowest weight pseudocodewords, which is advantageous in comparison with the one discussed previously, in particular because of being provably monotonic and also resulting in more frequent discoveries of pseudo-codewords with the lowest weights. The algorithm performance is tested on the example of the Tanner [155, 64, code over the Additive White Gaussian Noise (AWGN) channel.

Searching for low weight pseudo-codewords

2007 Information Theory and Applications Workshop, 2007

Photoexcited wavepacket scattering on conical intersections: Semiclassical expansion

by Misha Stepanov and Vladimir Chernyak

Notes about Passive Scalar in Large-Scale Velocity Field

Predicting failures in power grids

Detuning characteristics of ionic anti-Stokes Raman laser

Continuous-wave generation is demonstrated of the anti- Stokes Raman laser in new (Alpha) scheme ... more Continuous-wave generation is demonstrated of the anti- Stokes Raman laser in new (Alpha) scheme ArII 3d'2G9/2 yields 4p'2F7/2 yields 4s'2D5/2 with long- lived start and final levels. Red pump radiation with wavelength (lambda) p equals 611 nm from a dye laser that excites transition 3d'2G9/2 yields 4p'2F7/2 is converted into the blue radiation at (lambda) equals 461 nm (4p'2F7/2 yields

Pseudo-codeword Landscape

2007 IEEE International Symposium on Information Theory, 2007

We discuss the performance of Low-Density-Parity-Check (LDPC) codes decoded by means of Linear Pr... more We discuss the performance of Low-Density-Parity-Check (LDPC) codes decoded by means of Linear Programming (LP) at moderate and large Signal-to-Noise-Ratios (SNR). Utilizing a combination of the previously introduced pseudocodeword-search method and a new "dendro" trick, which allows us to reduce the complexity of the LP decoding, we analyze the dependence of the Frame-Error-Rate (FER) on the SNR. Under Maximum-A-Posteriori (MAP) decoding the dendro-code, having only checks with connectivity degree three, performs identically to its original code with high-connectivity checks. For a number of popular LDPC codes performing over the Additive-White-Gaussian-Noise (AWGN) channel we found that either an errorfloor sets at a relatively low SNR, or otherwise a transient asymptote, characterized by a faster decay of FER with the SNR increase, precedes the error-floor asymptote. We explain these regimes in terms of the pseudo-codeword spectra of the codes.

Analysis of error floors of LDPC codes under LP decoding over the BSC

2009 IEEE International Symposium on Information Theory, 2009

... Analysis of Error Floors of LDPC Codes under LP Decoding over the BSC Shashi Kiran Chilappaga... more

Instanton method of post-error-correction analytical evaluation

by Misha Stepanov and Vladimir Chernyak

Manufacturing Engineer, 2004

We present a theoretical tool for evalu a t i o n of the error codes' p e r f o r m a n c e on gr... more We present a theoretical tool for evalu a t i o n of the error codes' p e r f o r m a n c e on graphs. T h e m e t h o d is k n o w n u n d e r the n a m e of instanton calculus and is c o m m o n i n theoretical physics. We introduce the i n s t a n t o n calculus for linear block codes, a n d give a closed f o r m expression for t h e b i t error rate for a class of codes whose graphical m o d e l is a p p r o x i m a t e d locally by a tree.

Diagnosis of Weaknesses in Modern Error Correction Codes: A Physics Approach

by Misha Stepanov and Vladimir Chernyak

Physical Review Letters, 2005

One of the main obstacles to the wider use of the modern error-correction codes is that, due to t... more One of the main obstacles to the wider use of the modern error-correction codes is that, due to the complex behavior of their decoding algorithms, no systematic method which would allow characterization of the bit-error-rate (BER) is known. This is especially true at the weak noise where many systems operate and where coding performance is difficult to estimate because of the diminishingly small number of errors. We show how the instanton method of physics allows one to solve the problem of BER analysis in the weak noise range by recasting it as a computationally tractable minimization problem.

Semiclassical Scattering on Conical Intersections

by Misha Stepanov and Vladimir Chernyak

Physical Review Letters, 2005

We apply a semiclassical approach to the scattering problem of a vibrational wave packet in the v... more We apply a semiclassical approach to the scattering problem of a vibrational wave packet in the vicinity of a conical intersection of electronic energy surfaces and derive analytical expressions for the scattering matrix. The latter are valid when the scattering length that scales as @ p is small and a wave packet passes through the scattering region with a constant velocity. The analytical results are in excellent agreement with numerical simulations for a realistic set of parameters.

Error Correction on a Tree: An Instanton Approach

by Misha Stepanov and Vladimir Chernyak

Physical Review Letters, 2004

We introduce a method that allows analytical or semianalytical estimating of the post-error corre... more We introduce a method that allows analytical or semianalytical estimating of the post-error correction bit error rate (BER) when a forward-error correction is utilized for transmitting information through a noisy channel. The generic method that applies to a variety of error-correction schemes in the regimes where the BER is low is illustrated using the example of a finite-size code approximated by a treelike structure. Exploring the statistical physics formulation of the problem we find that the BER decreases with the signal-to-noise ratio nonuniformly, i.e., crossing over through a sequence of phases. The higher the signal-to-noise ratio the lower the symmetry of the phase dominating BER.

New bisoliton solutions in dispersion managed systems

Physica D: Nonlinear Phenomena, 2009

In this paper we propose a method which provides a full description of solitary wave solutions of... more In this paper we propose a method which provides a full description of solitary wave solutions of the Schrödinger equation with periodically varying dispersion. This method is based on analysis and polynomial deformation of the spectrum of an iterative map. Using this method we discover a new family of antisymmetric bisoliton solutions. In addition to the fact that these solutions are of interest for nonlinear fiber optics and the theory of nonlinear Schrödinger equations with periodic coefficients, they have potential applications for increasing of bit-rate in high speed optical fiber communications.

Role of interaction in causing errors in optical soliton transmission

Optics Letters, 2002

We consider two solitons propagating under a filter-control scheme and describe the timing jitter... more We consider two solitons propagating under a filter-control scheme and describe the timing jitter that is caused by spontaneous-emission noise and enhanced by attraction between solitons. We find the bit-error rate as a function of system parameters (filtering and noise level), timing, initial distance, and the phase difference between solitons.