Capacity-Achieving Distributions in Gaussian Multiple Access Channel With Peak Power Constraints

Mamandipoor, Babak; Moshksar, Kamyar; Khandani, Amir K.

doi:10.1109/tit.2014.2342218

Cited by 31 publications

(17 citation statements)

References 14 publications

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“…Proof. To see (35) and (36), observe that Ξ A (x; P X ⋆ ), defined in (31), can be written as follows:…”

Section: B Connecting the Number Of Oscillations Of F Y ⋆ To The Nummentioning

confidence: 99%

“…Finally, it would interesting to see if the results of this paper can be extended to multiuser channels such as a multiple access channel with an amplitude constraint on the inputs where it is known that the discrete inputs are sum-capacity optimal [36], yet there are no bounds on the number of mass points of the optimal inputs.…”

Section: Proof Of the Lower Bound In (8)mentioning

confidence: 99%

See 1 more Smart Citation

The Capacity Achieving Distribution for the Amplitude Constrained Additive Gaussian Channel: An Upper Bound on the Number of Mass Points

Dytso

Yagli

Poor

et al. 2020

IEEE Trans. Inform. Theory

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This paper studies an n-dimensional additive Gaussian noise channel with a peak-power-constrained input. It is well known that, in this case, when n = 1 the capacity-achieving input distribution is discrete with finitely many mass points, and when n > 1 the capacity-achieving input distribution is supported on finitely many concentric shells. However, due to the previous proof technique, not even a bound on the exact number of mass points/shells was available. This paper provides an alternative proof of the finiteness of the number mass points/shells of the capacity-achieving input distribution while producing the first firm bounds on the number of mass points and shells, paving an alternative way for approaching many such problems.The first main result of this paper is an order tight implicit bound which shows that the number of mass points in the capacity-achieving input distribution is within a factor of two from the number of zeros of the downward shifted capacityachieving output probability density function. Next, this implicit bound is utilized to provide a first firm upper on the support size of optimal input distribution, an O(A 2 ) upper bound where A denotes the constraint on the input amplitude. The second main result of this paper generalizes the first one to the case when n > 1, showing that, for each and every dimension n ≥ 1, the number of shells that the optimal input distribution contains is O(A 2 ). Finally, the third main result of this paper reconsiders the case n = 1 with an additional average power constraint, demonstrating a similar O(A 2 ) bound.

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“…Proof. To see (35) and (36), observe that Ξ A (x; P X ⋆ ), defined in (31), can be written as follows:…”

Section: B Connecting the Number Of Oscillations Of F Y ⋆ To The Nummentioning

confidence: 99%

Section: Proof Of the Lower Bound In (8)mentioning

confidence: 99%

The Capacity Achieving Distribution for the Amplitude Constrained Additive Gaussian Channel: An Upper Bound on the Number of Mass Points

Dytso

Yagli

Poor

et al. 2020

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

show abstract

“…In [6], a point to point real scalar channel is considered in which sufficient conditions for the additive noise are provided such that the support of the optimal bounded input has a finite number of mass points. These sufficient conditions are also useful in multi-user settings as shown in [7] for the MAC channel under bounded inputs.…”

Section: Introductionmentioning

confidence: 99%

On the Capacity of Vector Gaussian Channels With Bounded Inputs

Rassouli

Clerckx

2016

IEEE Trans. Inform. Theory

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Abstract-The capacity of a deterministic multiple-input multiple-output (MIMO) channel under the peak and average power constraints is investigated. For the identity channel matrix, the approach of Shamai et al. is generalized to the higher dimension settings to derive the necessary and sufficient conditions for the optimal input probability density function. This approach prevents the usage of the identity theorem of the holomorphic functions of several complex variables which seems to fail in the multi-dimensional scenarios. It is proved that the support of the capacity-achieving distribution is a finite set of hyper-spheres with mutual independent phases and amplitude in the spherical domain. Subsequently, it is shown that when the average power constraint is relaxed, if the number of antennas is large enough, the capacity has a closed form solution and constant amplitude signaling at the peak power achieves it. Moreover, it will be observed that in a discrete-time memoryless Gaussian channel, the average power constrained capacity, which results from a Gaussian input distribution, can be closely obtained by an input where the support of its magnitude is a discrete finite set. Finally, we investigate some upper and lower bounds for the capacity of the non-identity channel matrix and evaluate their performance as a function of the condition number of the channel.

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“…Using this result, numerical examples of the low-power capacity region of the peak-power constrained Gaussian MAC have been provided in [34]. In [34] and [35], it has been proved that the boundary of the capacity region of the peak-power constrained Gaussian MAC is achieved by discrete input distributions with a finite number of mass points; however, no explicit outer or inner bounds on [14] Outer Bound C [3] [14]…”

Section: Asymptotic Analysis and Numerical Resultsmentioning

confidence: 99%

Bounds on the Capacity Region of the Optical Intensity Multiple Access Channel

Zhou

Zhang

2019

IEEE Trans. Commun.

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This paper provides new inner and outer bounds on the capacity region of the optical intensity multiple access channel (OIMAC) with a per-user average-or peak-power constraint. For the average-power constrained OIMAC, our bounds at high power are asymptotically tight, thereby characterizing the asymptotic capacity region. The bounds are extended to the Kuser OIMAC with an average-power constraint without loss of asymptotic optimality. For the peak-power constrained OIMAC, at high power, we bound the asymptotic capacity region to within 0.09 bits, and determine the asymptotic capacity region in the symmetric case. At moderate power, for both types of constraints, the capacity regions are bounded to within fairly small gaps.

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Capacity-Achieving Distributions in Gaussian Multiple Access Channel With Peak Power Constraints

Cited by 31 publications

References 14 publications

The Capacity Achieving Distribution for the Amplitude Constrained Additive Gaussian Channel: An Upper Bound on the Number of Mass Points

The Capacity Achieving Distribution for the Amplitude Constrained Additive Gaussian Channel: An Upper Bound on the Number of Mass Points

On the Capacity of Vector Gaussian Channels With Bounded Inputs

Bounds on the Capacity Region of the Optical Intensity Multiple Access Channel

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