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Sergio Verdu - One of the best experts on this subject based on the ideXlab platform.
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on Channel Dispersion per unit cost
International Symposium on Information Theory, 2016Co-Authors: Yucel Altug, Vincent H Poor, Sergio VerduAbstract:The fundamental tradeoff of Channel coding per unit cost in the fixed-error probability regime is investigated for discrete memoryless Channels in the presence of a free input symbol. The speed of convergence to the capacity per unit cost in the absence of feedback is characterized in terms of a characteristic of the Channel and cost function, which is referred to as e-Dispersion per unit cost. Further, a sufficient condition for feedback to improve this convergence speed is provided.
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lossy joint source Channel coding in the finite blocklength regime
IEEE Transactions on Information Theory, 2013Co-Authors: Victoria Kostina, Sergio VerduAbstract:This paper finds new tight finite-blocklength bounds for the best achievable lossy joint source-Channel code rate, and demonstrates that joint source-Channel code design brings considerable performance advantage over a separate one in the nonasymptotic regime. A joint source-Channel code maps a block of k source symbols onto a length-n Channel codeword, and the fidelity of reproduction at the receiver end is measured by the probability e that the distortion exceeds a given threshold d. For memoryless sources and Channels, it is demonstrated that the parameters of the best joint source-Channel code must satisfy nC - kR(d) ≈ √(nV + k V(d)) Q-1(e), where C and V are the Channel capacity and Channel Dispersion, respectively; R(d) and V(d) are the source rate-distortion and rate-Dispersion functions; and Q is the standard Gaussian complementary cumulative distribution function. Symbol-by-symbol (uncoded) transmission is known to achieve the Shannon limit when the source and Channel satisfy a certain probabilistic matching condition. In this paper, we show that even when this condition is not satisfied, symbol-by-symbol transmission is, in some cases, the best known strategy in the nonasymptotic regime.
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lossy joint source Channel coding in the finite blocklength regime
arXiv: Information Theory, 2012Co-Authors: Victoria Kostina, Sergio VerduAbstract:This paper finds new tight finite-blocklength bounds for the best achievable lossy joint source-Channel code rate, and demonstrates that joint source-Channel code design brings considerable performance advantage over a separate one in the non-asymptotic regime. A joint source-Channel code maps a block of $k$ source symbols onto a length$-n$ Channel codeword, and the fidelity of reproduction at the receiver end is measured by the probability $\epsilon$ that the distortion exceeds a given threshold $d$. For memoryless sources and Channels, it is demonstrated that the parameters of the best joint source-Channel code must satisfy $nC - kR(d) \approx \sqrt{nV + k \mathcal V(d)} Q(\epsilon)$, where $C$ and $V$ are the Channel capacity and Channel Dispersion, respectively; $R(d)$ and $\mathcal V(d)$ are the source rate-distortion and rate-Dispersion functions; and $Q$ is the standard Gaussian complementary cdf. Symbol-by-symbol (uncoded) transmission is known to achieve the Shannon limit when the source and Channel satisfy a certain probabilistic matching condition. In this paper we show that even when this condition is not satisfied, symbol-by-symbol transmission is, in some cases, the best known strategy in the non-asymptotic regime.
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scalar coherent fading Channel Dispersion analysis
International Symposium on Information Theory, 2011Co-Authors: Yury Polyanskiy, Sergio VerduAbstract:The backoff from capacity due to finite blocklength can be assessed accurately from the Channel Dispersion. This paper analyzes the Dispersion of a single-user, scalar, coherent fading Channel with additive Gaussian noise. We obtain a convenient two-term expression for the Channel Dispersion which shows that, unlike the capacity, it depends crucially on the dynamics of the fading process.
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Channel Coding Rate in the Finite Blocklength Regime
IEEE Transactions on Information Theory, 2010Co-Authors: Yury Polyanskiy, H. Vincent Poor, Sergio VerduAbstract:This paper investigates the maximal Channel coding rate achievable at a given blocklength and error probability. For general classes of Channels new achievability and converse bounds are given, which are tighter than existing bounds for wide ranges of parameters of interest, and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100. It is also shown analytically that the maximal rate achievable with error probability ? isclosely approximated by C - ?(V/n) Q-1(?) where C is the capacity, V is a characteristic of the Channel referred to as Channel Dispersion , and Q is the complementary Gaussian cumulative distribution function.
Yury Polyanskiy - One of the best experts on this subject based on the ideXlab platform.
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coherent multiple antenna block fading Channels at finite blocklength
IEEE Transactions on Information Theory, 2019Co-Authors: Austin Collins, Yury PolyanskiyAbstract:In this paper, we consider a Channel model that is often used to describe mobile wireless scenarios: multiple-antenna additive white Gaussian noise Channels subject to random (fading) gains with full Channel state information at the receiver. The dynamics of the fading process are approximated by a piecewise-constant process (frequency non-selective isotropic block fading). This paper addresses the finite blocklength fundamental limits of this Channel model. Specifically, we give a formula for the Channel Dispersion—a quantity governing the delay required to achieve capacity. The multiplicative nature of the fading disturbance leads to a number of interesting technical difficulties that required us to enhance traditional methods for finding the Channel Dispersion. Alas, one difficulty remains: the converse (impossibility) part of our result holds under an extra constraint on the growth of the peak-power with blocklength. Our results demonstrate, for example, that while the capacities of $n_{t}\times n_{r}$ and $n_{r} \times n_{t}$ antenna configurations coincide (under fixed received power), the coding delay can be sensitive to this switch. For example, at the received SNR of 20 dB, the $16\times 100$ system achieves capacity with codes of length (delay) which is only 60% of the length required for the $100\times 16$ system. Another interesting implication is that for the MISO Channel, the Dispersion-optimal coding schemes require employing orthogonal designs such as Alamouti’s scheme—a surprising observation considering the fact that Alamouti’s scheme was designed for reducing demodulation errors, not improving coding rate. Finding these Dispersion-optimal coding schemes naturally gives a criteria for producing orthogonal design-like inputs in dimensions where orthogonal designs do not exist.
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coherent multiple antenna block fading Channels at finite blocklength
arXiv: Information Theory, 2017Co-Authors: Austin Collins, Yury PolyanskiyAbstract:In this paper we consider a Channel model that is often used to describe the mobile wireless scenario: multiple-antenna additive white Gaussian noise Channels subject to random (fading) gain with full Channel state information at the receiver. Dynamics of the fading process are approximated by a piecewise-constant process (frequency non-selective isotropic block fading). This work addresses the finite blocklength fundamental limits of this Channel model. Specifically, we give a formula for the Channel Dispersion -- a quantity governing the delay required to achieve capacity. Multiplicative nature of the fading disturbance leads to a number of interesting technical difficulties that required us to enhance traditional methods for finding Channel Dispersion. Alas, one difficulty remains: the converse (impossibility) part of our result holds under an extra constraint on the growth of the peak-power with blocklength. Our results demonstrate, for example, that while capacities of $n_t\times n_r$ and $n_r \times n_t$ antenna configurations coincide (under fixed received power), the coding delay can be quite sensitive to this switch. For example, at the received SNR of $20$ dB the $16\times 100$ system achieves capacity with codes of length (delay) which is only $60\%$ of the length required for the $100\times 16$ system. Another interesting implication is that for the MISO Channel, the Dispersion-optimal coding schemes require employing orthogonal designs such as Alamouti's scheme -- a surprising observation considering the fact that Alamouti's scheme was designed for reducing demodulation errors, not improving coding rate. Finding these Dispersion-optimal coding schemes naturally gives a criteria for producing orthogonal design-like inputs in dimensions where orthogonal designs do not exist.
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A beta-beta achievability bound with applications
2016 IEEE International Symposium on Information Theory (ISIT), 2016Co-Authors: Wei Yang, Yury Polyanskiy, Austin Collins, Giuseppe Durisi, Vincent H PoorAbstract:A Channel coding achievability bound expressed in terms of the ratio between two Neyman-Pearson β functions is proposed. This bound is the dual of a converse bound established earlier by Polyanskiy and Verdú (2014). The new bound turns out to simplify considerably the analysis in situations where the Channel output distribution is not a product distribution, for example due to a cost constraint or a structural constraint (such as orthogonality or constant composition) on the Channel inputs. Connections to existing bounds in the literature are discussed. The bound is then used to derive 1) the Channel Dispersion of additive non-Gaussian noise Channels with random Gaussian codebooks, 2) the Channel Dispersion of an exponential-noise Channel, 3) a second-order expansion for the minimum energy per bit of an additive white Gaussian noise Channel, and 4) a lower bound on the maximum coding rate of a multiple-input multiple-output Rayleigh-fading Channel with perfect Channel state information at the receiver, which is the tightest known achievability result.
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Dispersion of the coherent mimo block fading Channel
International Symposium on Information Theory, 2016Co-Authors: Austin Collins, Yury PolyanskiyAbstract:In this paper we consider a Channel model that is often used to describe the mobile wireless scenario: multiple-antenna additive white Gaussian noise Channels subject to random (fading) gain with full Channel state information at the receiver. Dynamics of the fading process are approximated by a piecewise-constant process (frequency non-selective isotropic block fading). This work addresses the finite blocklength fundamental limits of this Channel model. Specifically, we give a formula for the Channel Dispersion - a quantity governing the delay required to achieve capacity - and present achievability and (partial) converse bounds. Multiplicative nature of the fading disturbance leads to a number of interesting technical difficulties that required us to enhance traditional methods for finding Channel Dispersion. Knowledge of Channel Dispersion opens the possibility for studying the impact of Channel dynamics, antenna selection rules, etc on the communication rate.
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Dispersion of quasi static mimo fading Channels via stokes theorem
International Symposium on Information Theory, 2014Co-Authors: Wei Yang, Tobias Koch, Giuseppe Durisi, Yury PolyanskiyAbstract:This paper analyzes the Channel Dispersion of quasi-static multiple-input multiple-output fading Channels with no Channel state information at the transmitter. We show that the Channel Dispersion is zero under mild conditions on the fading distribution. The proof of our result is based on Stokes' theorem, which deals with the integration of differential forms on manifolds with boundary.
A Bononi - One of the best experts on this subject based on the ideXlab platform.
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a unified design framework for single Channel Dispersion managed terrestrial systems
Journal of Lightwave Technology, 2008Co-Authors: A Bononi, P Serena, A OrlandiniAbstract:This paper provides a unified framework to the design, performance optimization, and accurate numerical simulation of periodic, Dispersion-managed (DM) single-Channel long-haul optical transmission systems for nonsoliton on-off keying (OOK) modulation. The focus is on DM terrestrial systems, with identical spans composed of a long transmission fiber compensated at the span end by a linear Dispersion compensating module, with pre- and postcompensation fibers at the beginning and end of the link. The framework is based on the Dispersion-managed nonlinear Schrodinger equation (DM-NLSE). First, expressions of the DM-NLSE kernel are provided both in the frequency and the time domain, and a novel map strength parameter, appropriate for terrestrial systems, is introduced. It is then shown that the DM-NLSE contains all the basic information needed for system design, as summarized by three parameters: i) nonlinear phase, ii) in-line Dispersion, and iii) map strength. Through a large-signal perturbative analysis of the DM-NLSE, the well-known linear relationship between the in-line Dispersion and the optimal precompensation is derived, along with the large-signal step response of the DM link, from which the ghost pulses energy growth and a first estimation of the link memory are derived. The DM-NLSE is then linearized around the average signal field to get the amplitude/phase small-signal system matrix of the overall DM link, including pre- and postcompensation. By a singular-value decomposition of the small-signal DM link matrix, a novel expression of the memory of the optimized DM link is finally provided. Knowledge of such a memory is mandatory to run accurate numerical simulations and laboratory measurements with a sufficiently long pseudorandom bit sequence to avoid patterning effects.
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parametric gain approach to the analysis of single Channel dpsk dqpsk systems with nonlinear phase noise
Journal of Lightwave Technology, 2006Co-Authors: P Serena, A Orlandini, A BononiAbstract:This paper presents a novel method based on a parametric gain (PG) approach to study the impact of nonlinear phase noise in single-Channel Dispersion-managed differentially phase-modulated systems. This paper first shows through Monte Carlo simulations that the received amplified spontaneous emission (ASE) noise statistics, before photodetection, can be reasonably assumed to be Gaussian, provided a sufficiently large chromatic Dispersion is present in the transmission fiber. This paper then evaluates in a closed form the ASE power spectral density by linearizing the interaction between a signal and a noise in the limit of a distributed system. Even if the received ASE is nonstationary in time due to pulse shape and modulation, this paper shows that it can be approximated by an equivalent stationary process, as if the signal were continuous wave (CW). This paper then applies the CW-equivalent ASE model to bit-error-rate evaluation by using an extension of a known Karhunen-Loe/spl acute/ve method for quadratic detectors in colored Gaussian noise. Such a method avoids calculation of the nonlinear phase statistics and accounts for intersymbol interference due to a nonlinear waveform distortion and optical and electrical postdetection filtering. This paper compares binary and quaternary schemes with both nonreturn- and return-to-zero (RZ) pulses for various values of nonlinear phases and bit rates. The results confirm that PG deeply affects the system performance, especially with RZ pulses and with quaternary schemes. This paper also compares ON-OFF keying (OOK) differential phase-shifted keying (DPSK) systems, showing that the initial 3-dB advantage of DPSK is lost for increasing nonlinear phases because DPSK is less robust to PG than OOK.
A Orlandini - One of the best experts on this subject based on the ideXlab platform.
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a unified design framework for single Channel Dispersion managed terrestrial systems
Journal of Lightwave Technology, 2008Co-Authors: A Bononi, P Serena, A OrlandiniAbstract:This paper provides a unified framework to the design, performance optimization, and accurate numerical simulation of periodic, Dispersion-managed (DM) single-Channel long-haul optical transmission systems for nonsoliton on-off keying (OOK) modulation. The focus is on DM terrestrial systems, with identical spans composed of a long transmission fiber compensated at the span end by a linear Dispersion compensating module, with pre- and postcompensation fibers at the beginning and end of the link. The framework is based on the Dispersion-managed nonlinear Schrodinger equation (DM-NLSE). First, expressions of the DM-NLSE kernel are provided both in the frequency and the time domain, and a novel map strength parameter, appropriate for terrestrial systems, is introduced. It is then shown that the DM-NLSE contains all the basic information needed for system design, as summarized by three parameters: i) nonlinear phase, ii) in-line Dispersion, and iii) map strength. Through a large-signal perturbative analysis of the DM-NLSE, the well-known linear relationship between the in-line Dispersion and the optimal precompensation is derived, along with the large-signal step response of the DM link, from which the ghost pulses energy growth and a first estimation of the link memory are derived. The DM-NLSE is then linearized around the average signal field to get the amplitude/phase small-signal system matrix of the overall DM link, including pre- and postcompensation. By a singular-value decomposition of the small-signal DM link matrix, a novel expression of the memory of the optimized DM link is finally provided. Knowledge of such a memory is mandatory to run accurate numerical simulations and laboratory measurements with a sufficiently long pseudorandom bit sequence to avoid patterning effects.
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parametric gain approach to the analysis of single Channel dpsk dqpsk systems with nonlinear phase noise
Journal of Lightwave Technology, 2006Co-Authors: P Serena, A Orlandini, A BononiAbstract:This paper presents a novel method based on a parametric gain (PG) approach to study the impact of nonlinear phase noise in single-Channel Dispersion-managed differentially phase-modulated systems. This paper first shows through Monte Carlo simulations that the received amplified spontaneous emission (ASE) noise statistics, before photodetection, can be reasonably assumed to be Gaussian, provided a sufficiently large chromatic Dispersion is present in the transmission fiber. This paper then evaluates in a closed form the ASE power spectral density by linearizing the interaction between a signal and a noise in the limit of a distributed system. Even if the received ASE is nonstationary in time due to pulse shape and modulation, this paper shows that it can be approximated by an equivalent stationary process, as if the signal were continuous wave (CW). This paper then applies the CW-equivalent ASE model to bit-error-rate evaluation by using an extension of a known Karhunen-Loe/spl acute/ve method for quadratic detectors in colored Gaussian noise. Such a method avoids calculation of the nonlinear phase statistics and accounts for intersymbol interference due to a nonlinear waveform distortion and optical and electrical postdetection filtering. This paper compares binary and quaternary schemes with both nonreturn- and return-to-zero (RZ) pulses for various values of nonlinear phases and bit rates. The results confirm that PG deeply affects the system performance, especially with RZ pulses and with quaternary schemes. This paper also compares ON-OFF keying (OOK) differential phase-shifted keying (DPSK) systems, showing that the initial 3-dB advantage of DPSK is lost for increasing nonlinear phases because DPSK is less robust to PG than OOK.
P Serena - One of the best experts on this subject based on the ideXlab platform.
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a unified design framework for single Channel Dispersion managed terrestrial systems
Journal of Lightwave Technology, 2008Co-Authors: A Bononi, P Serena, A OrlandiniAbstract:This paper provides a unified framework to the design, performance optimization, and accurate numerical simulation of periodic, Dispersion-managed (DM) single-Channel long-haul optical transmission systems for nonsoliton on-off keying (OOK) modulation. The focus is on DM terrestrial systems, with identical spans composed of a long transmission fiber compensated at the span end by a linear Dispersion compensating module, with pre- and postcompensation fibers at the beginning and end of the link. The framework is based on the Dispersion-managed nonlinear Schrodinger equation (DM-NLSE). First, expressions of the DM-NLSE kernel are provided both in the frequency and the time domain, and a novel map strength parameter, appropriate for terrestrial systems, is introduced. It is then shown that the DM-NLSE contains all the basic information needed for system design, as summarized by three parameters: i) nonlinear phase, ii) in-line Dispersion, and iii) map strength. Through a large-signal perturbative analysis of the DM-NLSE, the well-known linear relationship between the in-line Dispersion and the optimal precompensation is derived, along with the large-signal step response of the DM link, from which the ghost pulses energy growth and a first estimation of the link memory are derived. The DM-NLSE is then linearized around the average signal field to get the amplitude/phase small-signal system matrix of the overall DM link, including pre- and postcompensation. By a singular-value decomposition of the small-signal DM link matrix, a novel expression of the memory of the optimized DM link is finally provided. Knowledge of such a memory is mandatory to run accurate numerical simulations and laboratory measurements with a sufficiently long pseudorandom bit sequence to avoid patterning effects.
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parametric gain approach to the analysis of single Channel dpsk dqpsk systems with nonlinear phase noise
Journal of Lightwave Technology, 2006Co-Authors: P Serena, A Orlandini, A BononiAbstract:This paper presents a novel method based on a parametric gain (PG) approach to study the impact of nonlinear phase noise in single-Channel Dispersion-managed differentially phase-modulated systems. This paper first shows through Monte Carlo simulations that the received amplified spontaneous emission (ASE) noise statistics, before photodetection, can be reasonably assumed to be Gaussian, provided a sufficiently large chromatic Dispersion is present in the transmission fiber. This paper then evaluates in a closed form the ASE power spectral density by linearizing the interaction between a signal and a noise in the limit of a distributed system. Even if the received ASE is nonstationary in time due to pulse shape and modulation, this paper shows that it can be approximated by an equivalent stationary process, as if the signal were continuous wave (CW). This paper then applies the CW-equivalent ASE model to bit-error-rate evaluation by using an extension of a known Karhunen-Loe/spl acute/ve method for quadratic detectors in colored Gaussian noise. Such a method avoids calculation of the nonlinear phase statistics and accounts for intersymbol interference due to a nonlinear waveform distortion and optical and electrical postdetection filtering. This paper compares binary and quaternary schemes with both nonreturn- and return-to-zero (RZ) pulses for various values of nonlinear phases and bit rates. The results confirm that PG deeply affects the system performance, especially with RZ pulses and with quaternary schemes. This paper also compares ON-OFF keying (OOK) differential phase-shifted keying (DPSK) systems, showing that the initial 3-dB advantage of DPSK is lost for increasing nonlinear phases because DPSK is less robust to PG than OOK.