Calculation of Mutual Information for Partially Coherent Gaussian Channels With Applications to Fiber Optics

Goebel, Bernhard; Essiambre, René-Jean; Kramer, Gerhard; Winzer, Peter J.; Hanik, Norbert

doi:10.1109/tit.2011.2162187

Cited by 60 publications

(74 citation statements)

References 34 publications

(94 reference statements)

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“…The transition probabilities depend on according to (7). In particular, the larger (strong phase noise), the more probable the transitions between "distant" states.…”

Section: Information Rate Analysismentioning

confidence: 99%

“…In this paper we present a comparison between discretetime models of the channel impaired by the Wiener phase noise [3] operating under different sampling rates. The Wiener phase noise yields a channel with memory and continuous state which has been studied in [4]- [7], by considering a discrete-time model in which the sampling rate is equal to the symbol rate. First, we consider the mean square error (MSE) as the comparison metric and we show how the choice of the sampling rate affects the difference between the models as a function of the phase noise intensity.…”

Section: Introductionmentioning

confidence: 99%

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On the information rate of phase noise-limited communications

Martalò

Tripodi

Raheli

2013

2013 Information Theory and Applications Workshop (ITA)

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Abstract-We discuss the accuracy of the time-discrete phase noise model described by a random walk with symbol-period spaced Gaussian increments. While this model is widely used for its simplicity, it is strictly valid in the slow phase regime only. It is customary to consider this model as a worst case, but a clear understanding of the phase dynamics which can be reliably represented may not be readily available.We address this problem by comparing the symbol-period spaced model with fractional-period spaced ones, which more reliably describe the physical system, in terms of the achievable information rate of the resulting phase noise channels. We show that indeed the symbol-period spaced model is a worst case that may offer a good modeling accuracy under a wide range of phase dynamics.

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“…The transition probabilities depend on according to (7). In particular, the larger (strong phase noise), the more probable the transitions between "distant" states.…”

Section: Information Rate Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the information rate of phase noise-limited communications

Martalò

Tripodi

Raheli

2013

2013 Information Theory and Applications Workshop (ITA)

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“…Multiplicative phase noise is one of the major impairments affecting the performance of coherent optical transmission systems [1][2][3]. Phase noise is due to both laser oscillators used for up-and down-conversion [4], and to crossphase modulation that arises in wavelength-division-multiplexing systems [5].…”

Section: Introductionmentioning

confidence: 99%

On discrete-time modeling of the filtered and symbol-rate sampled continuous-time signal affected by Wiener phase noise

Mandelli

Magarini

Spalvieri

et al. 2015

Optical Switching and Networking

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This paper investigates the differences between the symbol-spaced discrete-time Wiener phase noise channel model, commonly assumed in the literature to represent the effect of phase noise, and that obtained by symbol-rate sampling the filtered continuous-time received signal affected by continuous-time Wiener phase-noise. In particular, for comparison, we consider some statistical tests to check temporal and distributional properties of the two models. We show that the fit between the two models is very good even for quite strong values of phase noise. The main result is that when the standard deviation of the discrete-time Wiener phase noise increment σ P N is below a threshold of approximatelyσ P N ≃ 0.1 rad, the discrete-time Wiener model provides a good approximation to the actual symbol-spaced sampled filtered signal affected by continuous-time Wiener phase noise. We show that when σ P N is below σ P N the ratio between the power of the signal and the power of the model mismatch is greater than 20 dB. Simulation results are also presented to compare bit error rates of the two models in case of QPSK and 16-QAM transmission and to compare the power spectral densities of their associated complex exponential phase noises. Our results suggest that the discrete-time Wiener phase noise model can be adopted for many real-world systems, where, according to experimental results available in the literature, σ P N in the order of 0.1 rad is rarely found even when the nonlinearity of the optical channel is deeply stressed.

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“…Results on the capacity of the additive white Gaussian noise (AWGN) channel affected by memoryless multiplicative phase noise can be found in [10], [11]. The information rate transferred through the channel with memoryless phase noise is studied in [12], while considerations on the model for continuous-time memoryless phase noise are Copyright (c) 2014 IEEE. Personal use of this material is permitted.…”

Section: Introductionmentioning

confidence: 99%

“…) in (12). Note that the distribution p(s 0 ) of the initial state that, for k = 1, is the second factor inside the integral in the right side of (11), after a transient whose duration depends on the coherence time of the state process is forgotten.…”

mentioning

confidence: 99%

Upper and Lower Bounds to the Information Rate Transferred Through First-Order Markov Channels With Free-Running Continuous State

Barletta

Magarini

Pecorino

et al. 2014

IEEE Trans. Inform. Theory

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Abstract-Starting from the definition of mutual information, one promptly realizes that the probabilities inferred by Bayesian tracking can be used to compute the Shannon information between the state and the measurement of a dynamic system. In the Gaussian and linear case, the information rate can be evaluated from the probabilities computed by the Kalman filter. When the probability distributions inferred by Bayesian tracking are non tractable, one is forced to resort to approximated inference, which gives only an approximation to the wanted probabilities. We propose upper and lower bounds to the information rate between the hidden state and the measurement based on approximated inference. Application of these bounds to multiplicative communication channels is discussed, and experimental results for the discrete-time phase noise channel and for the GaussMarkov fading channel are presented.

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Calculation of Mutual Information for Partially Coherent Gaussian Channels With Applications to Fiber Optics

Cited by 60 publications

References 34 publications

On the information rate of phase noise-limited communications

On the information rate of phase noise-limited communications

On discrete-time modeling of the filtered and symbol-rate sampled continuous-time signal affected by Wiener phase noise

Upper and Lower Bounds to the Information Rate Transferred Through First-Order Markov Channels With Free-Running Continuous State

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