Abstract
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  28 Jan 2008 
Place of Publication  Eindhoven 
Publisher  
Print ISBNs  9789038617541 
DOIs  
Publication status  Published  2008 
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Bibliographical note
Proefschrift.Cite this
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Informationtheoretic analysis of a family of additive energy channels. / Martinez Vicente, A.
Eindhoven : Technische Universiteit Eindhoven, 2008. 215 p.Research output: Thesis › Phd Thesis 1 (Research TU/e / Graduation TU/e)
TY  THES
T1  Informationtheoretic analysis of a family of additive energy channels
AU  Martinez Vicente, A.
N1  Proefschrift.
PY  2008
Y1  2008
N2  This dissertation studies a new family of channel models for noncoherent com munications, the additive energy channels. By construction, the additive en ergy channels occupy an intermediate region between two widely used channel models: the discretetime Gaussian channel, used to represent coherent com munication systems operating at radio and microwave frequencies, and the discretetime Poisson channel, which often appears in the analysis of intensity modulated systems working at optical frequencies. The additive energy chan nels share with the Gaussian channel the additivity between a useful signal and a noise component. However, the signal and noise components are not complex valued quadrature amplitudes but, as in the Poisson channel, nonnegative real numbers, the energy or squared modulus of the complex amplitude. The additive energy channels come in two variants, depending on whether the channel output is discrete or continuous. In the former case, the energy is a multiple of a fundamental unit, the quantum of energy, whereas in the second the value of the energy can take on any nonnegative real number. For con tinuous output the additive noise has an exponential density, as for the energy of a sample of complex Gaussian noise. For discrete, or quantized, energy the signal component is randomly distributed according to a Poisson distribution whose mean is the signal energy of the corresponding Gaussian channel; part of the total noise at the channel output is thus a signaldependent, Poisson noise component. Moreover, the additive noise has a geometric distribution, the discrete counterpart of the exponential density. Contrary to the common engineering wisdom that not using the quadrature amplitude incurs in a signi¯cant performance penalty, it is shown in this dis sertation that the capacity of the additive energy channels essentially coincides with that of a coherent Gaussian model under a broad set of circumstances. Moreover, common modulation and coding techniques for the Gaussian chan nel often admit a natural extension to the additive energy channels, and their performance frequently parallels those of the Gaussian channel methods. Four informationtheoretic quantities, covering both theoretical and practi cal aspects of the reliable transmission of information, are studied: the channel capacity, the minimum energy per bit, the constrained capacity when a given digital modulation format is used, and the pairwise error probability. Of these quantities, the channel capacity sets a fundamental limit on the transmission capabilities of the channel but is sometimes di±cult to determine. The min imum energy per bit (or its inverse, the capacity per unit cost), on the other hand, turns out to be easier to determine, and may be used to analyze the performance of systems operating at low levels of signal energy. Closer to a practical ¯gure of merit is the constrained capacity, which estimates the largest amount of information which can be transmitted by using a speci¯c digital modulation format. Its study is complemented by the computation of the pairwise error probability, an e®ective tool to estimate the performance of practical coded communication systems. Regarding the channel capacity, the capacity of the continuous additive energy channel is found to coincide with that of a Gaussian channel with iden tical signaltonoise ratio. Also, an upper bound the tightest known to the capacity of the discretetime Poisson channel is derived. The capacity of the quantized additive energy channel is shown to have two distinct functional forms: if additive noise is dominant, the capacity is close to that of the continu ous channel with the same energy and noise levels; when Poisson noise prevails, the capacity is similar to that of a discretetime Poisson channel, with no ad ditive noise. An analogy with radiation channels of an arbitrary frequency, for which the quanta of energy are photons, is presented. Additive noise is found to be dominant when frequency is low and, simultaneously, the signaltonoise ratio lies below a threshold; the value of this threshold is well approximated by the expected number of quanta of additive noise. As for the minimum energy per nat (1 nat is log2 e bits, or about 1.4427 bits), it equals the average energy of the additive noise component for all the stud ied channel models. A similar result was previously known to hold for two particular cases, namely the discretetime Gaussian and Poisson channels. An extension of digital modulation methods from the Gaussian channels to the additive energy channel is presented, and their constrained capacity determined. Special attention is paid to their asymptotic form of the capacity at low and high levels of signal energy. In contrast to the behaviour in the vi Gaussian channel, arbitrary modulation formats do not achieve the minimum energy per bit at low signal energy. Analytic expressions for the constrained capacity at low signal energy levels are provided. In the highenergy limit simple pulseenergy modulations, which achieve a larger constrained capacity than their counterparts for the Gaussian channel, are presented. As a ¯nal element, the error probability of binary channel codes in the ad ditive energy channels is studied by analyzing the pairwise error probability, the probability of wrong decision between two alternative binary codewords. Saddlepoint approximations to the pairwise error probability are given, both for binary modulation and for bitinterleaved coded modulation, a simple and e±cient method to use binary codes with nonbinary modulations. The meth ods yield new simple approximations to the error probability in the fading Gaussian channel. The error rates in the continuous additive energy channel are close to those of coherent transmission at identical signaltonoise ratio. Constellations minimizing the pairwise error probability in the additive energy channels are presented, and their form compared to that of the constellations which maximize the constrained capacity at high signal energy levels.
AB  This dissertation studies a new family of channel models for noncoherent com munications, the additive energy channels. By construction, the additive en ergy channels occupy an intermediate region between two widely used channel models: the discretetime Gaussian channel, used to represent coherent com munication systems operating at radio and microwave frequencies, and the discretetime Poisson channel, which often appears in the analysis of intensity modulated systems working at optical frequencies. The additive energy chan nels share with the Gaussian channel the additivity between a useful signal and a noise component. However, the signal and noise components are not complex valued quadrature amplitudes but, as in the Poisson channel, nonnegative real numbers, the energy or squared modulus of the complex amplitude. The additive energy channels come in two variants, depending on whether the channel output is discrete or continuous. In the former case, the energy is a multiple of a fundamental unit, the quantum of energy, whereas in the second the value of the energy can take on any nonnegative real number. For con tinuous output the additive noise has an exponential density, as for the energy of a sample of complex Gaussian noise. For discrete, or quantized, energy the signal component is randomly distributed according to a Poisson distribution whose mean is the signal energy of the corresponding Gaussian channel; part of the total noise at the channel output is thus a signaldependent, Poisson noise component. Moreover, the additive noise has a geometric distribution, the discrete counterpart of the exponential density. Contrary to the common engineering wisdom that not using the quadrature amplitude incurs in a signi¯cant performance penalty, it is shown in this dis sertation that the capacity of the additive energy channels essentially coincides with that of a coherent Gaussian model under a broad set of circumstances. Moreover, common modulation and coding techniques for the Gaussian chan nel often admit a natural extension to the additive energy channels, and their performance frequently parallels those of the Gaussian channel methods. Four informationtheoretic quantities, covering both theoretical and practi cal aspects of the reliable transmission of information, are studied: the channel capacity, the minimum energy per bit, the constrained capacity when a given digital modulation format is used, and the pairwise error probability. Of these quantities, the channel capacity sets a fundamental limit on the transmission capabilities of the channel but is sometimes di±cult to determine. The min imum energy per bit (or its inverse, the capacity per unit cost), on the other hand, turns out to be easier to determine, and may be used to analyze the performance of systems operating at low levels of signal energy. Closer to a practical ¯gure of merit is the constrained capacity, which estimates the largest amount of information which can be transmitted by using a speci¯c digital modulation format. Its study is complemented by the computation of the pairwise error probability, an e®ective tool to estimate the performance of practical coded communication systems. Regarding the channel capacity, the capacity of the continuous additive energy channel is found to coincide with that of a Gaussian channel with iden tical signaltonoise ratio. Also, an upper bound the tightest known to the capacity of the discretetime Poisson channel is derived. The capacity of the quantized additive energy channel is shown to have two distinct functional forms: if additive noise is dominant, the capacity is close to that of the continu ous channel with the same energy and noise levels; when Poisson noise prevails, the capacity is similar to that of a discretetime Poisson channel, with no ad ditive noise. An analogy with radiation channels of an arbitrary frequency, for which the quanta of energy are photons, is presented. Additive noise is found to be dominant when frequency is low and, simultaneously, the signaltonoise ratio lies below a threshold; the value of this threshold is well approximated by the expected number of quanta of additive noise. As for the minimum energy per nat (1 nat is log2 e bits, or about 1.4427 bits), it equals the average energy of the additive noise component for all the stud ied channel models. A similar result was previously known to hold for two particular cases, namely the discretetime Gaussian and Poisson channels. An extension of digital modulation methods from the Gaussian channels to the additive energy channel is presented, and their constrained capacity determined. Special attention is paid to their asymptotic form of the capacity at low and high levels of signal energy. In contrast to the behaviour in the vi Gaussian channel, arbitrary modulation formats do not achieve the minimum energy per bit at low signal energy. Analytic expressions for the constrained capacity at low signal energy levels are provided. In the highenergy limit simple pulseenergy modulations, which achieve a larger constrained capacity than their counterparts for the Gaussian channel, are presented. As a ¯nal element, the error probability of binary channel codes in the ad ditive energy channels is studied by analyzing the pairwise error probability, the probability of wrong decision between two alternative binary codewords. Saddlepoint approximations to the pairwise error probability are given, both for binary modulation and for bitinterleaved coded modulation, a simple and e±cient method to use binary codes with nonbinary modulations. The meth ods yield new simple approximations to the error probability in the fading Gaussian channel. The error rates in the continuous additive energy channel are close to those of coherent transmission at identical signaltonoise ratio. Constellations minimizing the pairwise error probability in the additive energy channels are presented, and their form compared to that of the constellations which maximize the constrained capacity at high signal energy levels.
U2  10.6100/IR632385
DO  10.6100/IR632385
M3  Phd Thesis 1 (Research TU/e / Graduation TU/e)
SN  9789038617541
PB  Technische Universiteit Eindhoven
CY  Eindhoven
ER 