The capacity of average and peak-power-limited quadrature Gaussian channels

Shamai, Shlomo; Bar-David, I.

doi:10.1109/18.391243

Cited by 221 publications

(240 citation statements)

References 29 publications

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“…In [8] some comparison between squared QAM and circular APSK over linear channels was performed based on the computation of the error bound parameter, showing some minor potential advantage of APSK. Further work on mutual information for modulations with average and peak power constraints is reported in [9], which proves the advantages of circular APSK constellations under those power constraints. Mutual information performance loss for APSK in peak power limited Gaussian complex channels is reported in [10] and compared to classical QAM modulations; it is shown that under this assumption APSK considerably outperforms QAM in terms of mutual information, the gain particularly remarkable for 16-ary and 64-ary constellations.…”

Section: Introductionmentioning

confidence: 99%

Turbo-coded APSK modulations design for satellite broadband communications

Gaudenzi

Fàbregas

Martinez

2006

Int. J. Satell. Commun. Network.

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This paper investigates the design of power and spectrally efficient coded modulations based on Amplitude Phase Shift Keying (APSK) modulation with application to satellite broadband communications. APSK represents an attractive modulation format for digital transmission over nonlinear satellite channels due to its power and spectral efficiency combined with its inherent robustness against nonlinear distortion. For these reasons APSK has been very recently introduced in the new standard for satellite Digital Video Broadcasting named DVB-S2 [1]. Assuming an ideal rectangular transmission pulse, for which no nonlinear inter-symbol interference is present and perfect pre-compensation of the nonlinearity, we optimize the APSK constellation. In addition to the minimum distance criterion, we introduce a new optimization based on channel capacity; this new method generates an optimum constellation for each spectral efficiency. To achieve power efficiency jointly with low bit error rate (BER) floor we adopt a powerful binary serially concatenated turbo-code coupled with optimal APSK modulations through bit-interleaved coded modulation. We derive tight approximations on the maximumlikelihood decoding error probability, and results are compared with computer simulations. In Ref.[2], the current analysis is complemented with the effects related to satellite nonlinear distortion effects with a band-limited transmission pulse and including demodulator timing,

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Section: Introductionmentioning

confidence: 99%

Turbo-coded APSK modulations design for satellite broadband communications

Gaudenzi

Fàbregas

Martinez

2006

Int. J. Satell. Commun. Network.

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“…The algorithm 8 for finding the number, the positions and the probabilities of the optimal mass points is exactly the same as that explained in [2]. When the average power constraint is relaxed, figures 2 to 6 show the capacity of the channel in (2) Figure 7 shows the capacity of the four dimensional channel versus u p along with the optimal input for a fixed average power u a = 10.…”

Section: Numerical Resultsmentioning

confidence: 85%

“…In [2], Shamai and Bar-David gave a full account on the capacity of a quadrature Gaussian channel under the aforementioned constraints and proved that the optimal input distribution has a discrete amplitude and a uniform independent phase. This discreteness in the optimal input distribution was surprisingly shown in [3] to be true even without a peak power constraint for the Rayleigh-fading channel when no channel state information (CSI) is assumed either at the receiver or the transmitter.…”

Section: Introductionmentioning

confidence: 99%

On the capacity of vector Gaussian channels with bounded inputs

Rassouli¹,

Clerckx

2015

2015 IEEE International Conference on Communications (ICC)

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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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“…. , n [22]. Note that for a given code, the randomness in E[x 2 t (M )] ≤ P is only due to the message M .…”

Section: Continuous Channelsmentioning

confidence: 99%

Separation of Source-Network Coding and Channel Coding in Wireline Networks

Jalali

Effros

2015

IEEE Trans. Inform. Theory

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In this paper we prove the separation of source-network coding and channel coding in wireline networks. For the purposes of this work, a wireline network is any network of independent, memoryless, point-to-point, finite-alphabet channels used to transmit dependent sources either losslessly or subject to a distortion constraint. In deriving this result, we also prove that in a general memoryless network with dependent sources, lossless and zero-distortion reconstruction are equivalent provided that the conditional entropy of each source given the other sources is nonzero. Furthermore, we extend the separation result to the case of continuous-alphabet, point-to-point channels such as additive white Gaussian noise (AWGN) channels.

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The capacity of average and peak-power-limited quadrature Gaussian channels

Cited by 221 publications

References 29 publications

Turbo-coded APSK modulations design for satellite broadband communications

Turbo-coded APSK modulations design for satellite broadband communications

On the capacity of vector Gaussian channels with bounded inputs

Separation of Source-Network Coding and Channel Coding in Wireline Networks

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