Second-Order Asymptotics of Mutual Information

Prelov, V. V.; Verdú, S.

doi:10.1109/tit.2004.831784

Cited by 127 publications

(114 citation statements)

References 12 publications

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“…As for the entropy formula (1), when and are not defined on but on some measurable space (or are not second order), the main formula still holds provided that in (55) In addition to (2) giving the mutual information between a random variable and its Gaussian contaminated version, a relationship between mutual information and estimation had been found in [19] (65)…”

Section: Lemmamentioning

confidence: 99%

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Mismatched estimation and relative entropy

Verdú

2009

2009 IEEE International Symposium on Information Theory

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Abstract-A random variable with distribution is observed in Gaussian noise and is estimated by a mismatched minimum meansquare estimator that assumes that the distribution is , instead of . This paper shows that the integral over all signal-to-noise ratios (SNRs) of the excess mean-square estimation error incurred by the mismatched estimator is twice the relative entropy (in nats). This representation of relative entropy can be generalized to nonreal-valued random variables, and can be particularized to give new general representations of mutual information in terms of conditional means. Inspired by the new representation, we also propose a definition of free relative entropy which fills a gap in, and is consistent with, the literature on free probability.Index Terms-Divergence, free probability, minimum meansquare error (MMSE) estimation, mutual information, relative entropy, Shannon theory, statistics.

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Section: Lemmamentioning

confidence: 99%

“…where (113) is the (classical) relative entropy in (19). A representation for the free relative entropy (99) in terms of the R-transforms of and would be useful.…”

Section: Free Relative Entropymentioning

confidence: 99%

Mismatched estimation and relative entropy

Verdú

2009

2009 IEEE International Symposium on Information Theory

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“…In [7], Prelov and Verdú determined the coefficients c 1 and c 2 for the so-called proper-complex constellations introduced by Neeser and Massey [8], which satisfy…”

Section: A Coded Modulationmentioning

confidence: 99%

Bit-Interleaved Coded Modulation in the Wideband Regime

Martinez

Fàbregas²,

Caire

2007

2007 IEEE International Symposium on Information Theory

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The wideband regime of bit-interleaved coded modulation (BICM) in Gaussian channels is studied.The Taylor expansion of the coded modulation capacity for generic signal constellations at low signal-tonoise ratio (SNR) is derived and used to determine the corresponding expansion for the BICM capacity.Simple formulas for the minimum energy per bit and the wideband slope are given. BICM is found to be suboptimal in the sense that its minimum energy per bit can be larger than the corresponding value for coded modulation schemes. The minimum energy per bit using standard Gray mapping on M -PAM or M 2 -QAM is given by a simple formula and shown to approach -0.34 dB as M increases. Using the low SNR expansion, a general trade-off between power and bandwidth in the wideband regime is used to show how a power loss can be traded off against a bandwidth gain.A. Martinez and F. Willems are with the

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“…To name a few, this has been studied earlier in [28] which provides capacity expressions under "weak" input signals, in [29] which focuses on low-SNR second order asymptotics of channel capacity, and in [30] which discusses low SNR asymptotics using the relation between mutual information and minimum mean square error (MMSE) over Gaussian channels. In this context, the contribution of this work is characterizing the low-SNR asymptotic capacity of MIMO IM-DD channels and shedding light on the capacity achieving input in this regime.…”

Section: Introductionmentioning

confidence: 99%

Low-SNR Asymptotic Capacity of MIMO Optical Intensity Channels with Peak and Average Constraints

Chaaban

Rezki

Alouini

2018

IEEE Trans. Commun.

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Abstract-The low-SNR asymptotic capacity of the multipleinput multiple-output (MIMO) optical intensity channel is studied under both average and peak intensity constraints. We focus on low SNR, which can be modeled as the scenario where both constraints proportionally vanish, or where the peak constraint is held constant while the average constraint vanishes. A capacity upper bound is derived, and is shown to be tight at low SNR under both scenarios. The capacity achieving input distribution at low SNR is shown to be a maximally-correlated vectorbinary input distribution. Consequently, the low-SNR capacity of the channel is characterized. As a byproduct, it is shown that for a channel with peak intensity constraints only, or with peak intensity constraints and individual (per aperture) average intensity constraints, a simple scheme composed of coded onoff keying, spatial repetition, and maximum-ratio combining is optimal at low SNR.

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Second-Order Asymptotics of Mutual Information

Cited by 127 publications

References 12 publications

Mismatched estimation and relative entropy

Mismatched estimation and relative entropy

Bit-Interleaved Coded Modulation in the Wideband Regime

Low-SNR Asymptotic Capacity of MIMO Optical Intensity Channels with Peak and Average Constraints

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