On the Capacity of Vector Gaussian Channels With Bounded Inputs

Rassouli, Borzoo; Clerckx, Bruno

doi:10.1109/tit.2016.2615632

Cited by 31 publications

(31 citation statements)

References 16 publications

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“…As a matter of fact, this phenomena that the optimal input distribution lies on finitely many concentric spheres remains true for any n ≥ 2, cf. [4], [5] and [6].…”

Section: Introductionmentioning

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

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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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“…As a matter of fact, this phenomena that the optimal input distribution lies on finitely many concentric spheres remains true for any n ≥ 2, cf. [4], [5] and [6].…”

Section: Introductionmentioning

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

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“…However, only few antenna elements are required, for the hit in data rate to become negligibly small. In fact, it can be shown that for any fixed SNR in a MIMO system with bounded inputs, there exist a threshold for the number of antennas, beyond which the amplitude component of the vector signal does not contribute to mutual information [23]. The findings of Fig.…”

mentioning

confidence: 86%

(Continuous) Phase Modulation on the Hypersphere

Sedaghat

Müller

Rachinger

2016

IEEE Trans. Wireless Commun.

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We introduce Phase Modulation on the Hypersphere (PMH) for load-modulated Multiple-Input MultipleOutput (MIMO) transmitters with a single central power amplifier. In PMH, the peak to average ratio of the sum power before pulse shaping is 1, thus the central power amplifier of load-modulated MIMO transmitters does not require any backoff. We derive the capacity of PMH on an additive white Gaussian noise (AWGN) channel and show that the input signal should be uniformly distributed on a hypersphere. The mutual information of uniformly distributed PMH input is derived in an uplink multiple-access independent identically distributed (iid) Gaussian MIMO channel using the replica method from statistical physics.Furthermore, discrete PMH is introduced using spherical codes and also generalizing Minimum Shift Keying (MSK) from the complex unit circle to the hypersphere. We investigate different pulse shaping methods for PMH including a novel spherical filtering. Using spherical pulse shaping, the signal stays on the hypersphere. Various filters are investigated and a tradeoff between spectral shape and peak-to-average-sum-power ratio (PASPR) is found. For as few as 4 antennas, good spectral properties (similar to root-raised cosine pulses) can be achieved at very low PASPR. Both former and latter further improve with increasing the number of antennas.Index Terms-Continuous phase modulation (CPM), Gaussian multiple-access channel, minimum shift keying, multiple-input multiple-output (MIMO) systems, mutual information, replica analysis, spherical filtering.

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“…From the duality of channel coding and universal source coding (Chapter 13 in [20]), the solution of Q Y in (41) is the induced output distribution of the capacity-achieving distribution of this channel. The solution to this problem has been investigated in [24] and [25] and it has been shown 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. A uniform distribution on a single sphere is optimal as R √ n → 0 has been shown in [24].…”

Section: A Converse Bounds Under Maximal Power Constraintmentioning

confidence: 99%

“…The solution to this problem has been investigated in [24] and [25] and it has been shown 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. A uniform distribution on a single sphere is optimal as R √ n → 0 has been shown in [24]. In general case when R = √ nP and R/ √ n = √ P is a constant, the uniform distribution of the surface of the sphere is not optimal.…”

Section: A Converse Bounds Under Maximal Power Constraintmentioning

confidence: 99%

One-shot achievability and converse bounds of Gaussian random coding in AWGN channels under covert constraint

Wei

Luo

2019

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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It is well known that finite blocklength plays an important role in the analysis of practical communication. This paper considers the achievability and converse bounds on the maximal channel coding rate (throughput) at a given blocklength and error probability in covert communication over AWGN channels. The covert constraint is in the form of an upper bound of total variation distance (TVD). For the achievability, Gaussian random coding scheme is adopted for convenience in the analysis of TVD. The classical results of finite blocklength regime are not applicable in this case. By revisiting [18], we first present new and more general achievability bounds for random coding schemes under maximal or average probability of error requirements. The general bounds are then applied to covert communication in AWGN channels where codewords are generated from Gaussian distribution while meeting the maximal power constraint. We further show an interesting connection between attaining tight achievability and converse bounds and solving two total variation distance related minimax problems. Further comparison is made between the new achievability bound and existing one with deterministic codebooks. The TVD at the adversary is analyzed under the given coding scheme, and the power level induced by covert constraint is bounded by applications of divergence inequalities. Our thorough analysis thus leads us to a comprehensive characterization of the attainable throughput in covert communication over AWGN channels. The summary of the initial part of this paper was published in [29].

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On the Capacity of Vector Gaussian Channels With Bounded Inputs

Cited by 31 publications

References 16 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

(Continuous) Phase Modulation on the Hypersphere

One-shot achievability and converse bounds of Gaussian random coding in AWGN channels under covert constraint

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