Suchergebnisse

Russland kommt für das Inkrafttreten des Kioto-Protokolls eine Schlüsselrolle zu. Das Land zögert jedoch trotz einer großzügigen Emissionsrechtszuteilung und erheblicher weiterer Zugeständnisse mit der Ratifizierung. Worauf ist dies zurückzuführen?

Currently, international climate negotiations concentrate on design issues for the flexible instruments outlined in the Kyoto Protocol. As the 6th Conference of the Parties to the U.N. Framework Convention on Climate Change in late 2000 or early 2001 has to take decisions on these matters, it is imperative to develop solutions that combine long-term economic efficiency with long-term environmental effectiveness. Sometimes, a reconciliation of these targets is difficult and compromises have to be made. This report discusses solutions for three critical issues which have got different degrees of attention until now but are linked inasmuch their solution will be crucial for the success of the Kyoto Protocol. The authors have come across them due to their close involvement in the negotiation process. The first issue has been a major topic of debate - the possibility that Russia and other countries in transition may have an enormous surplus of emission permits due to their economic collapse. Unfettered trade in this surplus would artificially depress permit prices, reduce the incentive for long-term innovation and would not be linked to any efficiency improvement in the selling countries. Koch and Michaelowa discuss ways how incentives can be devised to link sales of emission permits with actions that lead to long-term emission reductions. They include an element of early action designed to prevent lock-in on an emission-intensive path of economic recovery by fostering investments whose emission reduction cannot be quantified but is nevertheless real. Early project-related Joint Implementation plays an important role in this context. The second issue is relatively technical but a necessary condition for the functioning of a global market in emission permits. It deals with the design of a system of national registries that track trades in permits. An International Registry would be the node of this system and guarantee that no fraudulent trades enter the system. A homogenous trading unit would be created. The way how trades are processed, the information requirements and the time-related aspect of the implementation of the registry system are discussed. Finally, the third issue seems remote but may prove challenging in the long term. International conflict will impact upon the Kyoto Protocol commitments. Wars like the one in Kosovo will lead to additional greenhouse gas emissions that have to be accounted for. Territorial changes will lead to changes in commitments. The authors discuss the different possibilities that change commitments and make recommendations how they could be accommodated in the Kyoto framework. Dr. Axel Michaelowa, a former staff member of HWWA Institute for Economic Research, is now working as an independent climate policy expert in Paris. Among other functions, he serves as a permanent advisor and project coordinator for HWWA on the economics of international climate policy. Tobias Koch is a specialist on Russian climate and energy policy. He is doing research with the Center for Energy Policy in Moscow and has also worked for the UN climate change secretariat on issues of emissions trading. However, the views expressed in this report are his personal ones.

Proceeding of: 2020 IEEE International Symposium on Information Theory (ISIT), Los Angeles, CA, USA, 21-26 June 2020 ; This paper concerns the maximum coding rate at which a code of given blocklength can be transmitted with a given block-error probability over a non-coherent Rayleigh block-fading channel with multiple transmit and receive antennas (MIMO). In particular, a high-SNR normal approximation of the maximum coding rate is presented, which is proved to become accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals L tend to infinity. ; C. Qi and T. Koch have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant No. 714161). T. Koch has further received funding from the Spanish Ministerio de Economía y Competitividad under Grants RYC-2014-16332 and TEC2016-78434-C3-3-R (AEI/FEDER, EU)

An earlier version of this paper was presented in part at the 2019 IEEE International Symposium on Information Theory [DOI:10.1109/ISIT.2019.8849751], in part at the 2020 International Zurich Seminar on Information and Communication [DOI:10.3929/ethz-b-000403243], and in part at the 2020 IEEE International Symposium on Information Theory [DOI:10.1109/ISIT44484.2020.9174091]. ; This paper considers a Gaussian multiple-access channel with random user activity where the total number of users ℓn and the average number of active users kn may grow with the blocklength n . For this channel, it studies the maximum number of bits that can be transmitted reliably per unit-energy as a function of ℓn and kn . When all users are active with probability one, i.e., ℓn=kn , it is demonstrated that, if kn is of an order strictly below n/logn , then each user can achieve the single-user capacity per unit-energy (loge)/N0 (where N0/2 is the noise power) by using an orthogonal-access scheme. In contrast, if kn is of an order strictly above n/logn , then the users cannot achieve any positive rate per unit-energy. Consequently, there is a sharp transition between orders of growth where interference-free communication is feasible and orders of growth where reliable communication at a positive rate per unit-energy is infeasible. It is further demonstrated that orthogonal-access schemes in combination with orthogonal codebooks, which achieve the capacity per unit-energy when the number of users is bounded, can be strictly suboptimal. When the user activity is random, i.e., when ℓn and kn are different, it is demonstrated that, if knlogℓn is sublinear in n , then each user can achieve the single-user capacity per unit-energy (loge)/N0 . Conversely, if knlogℓn is superlinear in n , then the users cannot achieve any positive rate per unit-energy. Consequently, there is again a sharp transition between orders of growth where interference-free communication is feasible and orders of growth where reliable communication at a positive rate is infeasible that depends on the asymptotic behaviors of both ℓn and kn . It is further demonstrated that orthogonal-ac. ; The work of Jithin Ravi was supported by the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Program under Grant 714161. The work of Tobias Koch was supported in part by the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Program under Grant 714161; and in part by the Spanish Ministerio de Ciencia e Innovación under Grant RYC-2014-16332, Grant TEC2016-78434-C3-3-R (AEI/FEDER, EU), and Grant PID2020-116683GB-C21 / AEI / 10.13039/501100011033.

Proceeding of: 55th Asilomar Conference on Signals, Systems, and Computers, October 31 - November 3, 2021 Pacific Grove, California, USA. ; In the emerging Internet of Things, a massive number of devices may connect to one common receiver. Consequently, models that study this setting are variants of the classical multiple-access channel where the number of users grows with the blocklength. Roughly, these models can be classified into three groups based on two criteria: the notion of probability of error and whether users use the same codebook. The first group follows the classical notion of probability of error and assumes that users use different codebooks. In the second group, users use different codebooks, but a new notion of probability of error called per-user probability of error is considered. The third group considers the per-user probability of error and that users are restricted to use the same codebook. This group is also known as unsourced random access. For the first and second groups of models, scaling laws that describe the capacity per unit-energy as a function of the order of growth of users were characterized by Ravi and Koch (arxiv.org/abs/2012.10350). In this paper, we first review these results. We then present scaling laws for the third group of models, i.e., unsourced random access. ; J. Ravi and T. Koch have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant No. 714161). T. Koch has further received funding from the Spanish Ministerio de Ciencia e Innovación under Grant PID2020-116683GB-C21 / AEI / 10.13039/501100011033.

Proceeding of: 2020 IEEE International Symposium on Information Theory (ISIT), Los Angeles, CA, USA, 21-26 June 2020 ; We consider a Gaussian multiple-access channel with random user activity where the total number of userslₙ and the average number of active users kₙ may be unbounded. For this channel, we characterize the maximum number of bits that can be transmitted reliably per unit-energy in terms of lₙ and kₙ . We show that if kₙ log lₙ is sublinear in n, then each user can achieve the single-user capacity per unit-energy. Conversely, if kₙ log lₙ is superlinear in n, then the capacity per unit-energy is zero. We further demonstrate that orthogonal-access schemes, which are optimal when all users are active with probability one, can be strictly suboptimal. ; J. Ravi and T. Koch have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant No. 714161). T. Koch has further received funding from the Spanish Ministerio de Economía y Competitividad under Grants RYC-2014-16332 and TEC2016-78434-C3-3-R (AEI/FEDER, EU).

In 1959, Rényi proposed the information dimension and the d-dimensional entropy to measure the information content of general random variables. This paper proposes a generalization of information dimension to stochastic processes by defining the information dimension rate as the entropy rate of the uniformly quantized stochastic process divided by minus the logarithm of the quantizer step size 1/m in the limit as m to infty. It is demonstrated that the information dimension rate coincides with the rate-distortion dimension, defined as twice the rate-distortion function R(D) of the stochastic process divided by -log (D) in the limit as D downarrow 0 . It is further shown that among all multivariate stationary processes with a given (matrix-valued) spectral distribution function (SDF), the Gaussian process has the largest information dimension rate and the information dimension rate of multivariate stationary Gaussian processes is given by the average rank of the derivative of the SDF. The presented results reveal that the fundamental limits of almost zero-distortion recovery via compressible signal pursuit and almost lossless analog compression are different in general. ; The work of Bernhard C. Geiger has partly been funded by the Erwin Schrödinger Fellowship J 3765 of the Austrian Science Fund and by the German Ministry of Education and Research in the framework of an Alexander von Humboldt Professorship. The Know-Center is funded within the Austrian COMET Program - Competence Centers for Excellent Technologies - under the auspices of the Austrian Federal Ministry of Transport, Innovation and Technology, the Austrian Federal Ministry of Digital and Economic Affairs, and by the State of Styria. COMET is managed by the Austrian Research Promotion Agency FFG. The work of Tobias Koch has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement number 714161), from the 7th European Union Framework Programme under Grant 333680, from the Ministerio de EconomÍa y Competitividad of Spain under Grants TEC2013-41718-R, RYC-2014-16332, and TEC2016-78434-C3-3-R (AEI/FEDER, EU), and from the Comunidad de Madrid under Grant S2103/ICE-2845.

Proceeding of: 2019 IEEE International Symposium on Information Theory (ISIT), 7-12 July 2019, Paris, France ; We consider a Gaussian multiple-access channel where the number of transmitters grows with the blocklength n. For this setup, the maximum number of bits that can be transmitted reliably per unit-energy is analyzed. We show that if the number of users is of an order strictly above n/log n, then the users cannot achieve any positive rate per unit-energy. In contrast, if the number of users is of order strictly below n/log n, then each user can achieve the single-user capacity per unit-energy (log e)/N 0 (where N 0 /2 is the noise power) by using an orthogonal access scheme such as time division multiple access. We further demonstrate that orthogonal codebooks, which achieve the capacity per unit-energy when the number of users is bounded, can be strictly suboptimal. ; J. Ravi and T. Koch have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant No. 714161). T. Koch has further received funding from the Spanish Ministerio de Economía y Competitividad under Grants RYC-2014-16332 and TEC2016-78434-C3-3-R (AEI/FEDER, EU).

The nonnegativity of relative entropy implies that the differential entropy of a random vector X with probability density function (pdf) f is upper-bounded by -E[log g(X)]for any arbitrary pdf g. Using this inequality with a cleverly chosen g, we derive a lower bound on the asymptotic excess rate of entropy-constrained vector quantization for d-dimensional sources and rth-power distortion, where the asymptotic excess rate is defined as the difference between the smallest output entropy of a vector quantizer satisfying the distortion constraint and the rate-distortion function in the limit as the distortion tends to zero. Specialized to the one-dimensional case, this lower bound coincides with the asymptotic excess rate achieved by a uniform quantizer, thereby recovering the result by Gish and Pierce that uniform quantizers are asymptotically optimal as the allowed distortion tends to zero. Furthermore, in the one-dimensional case, the derivation of the lower bound reveals a necessary condition for a sequence of quantizers to be asymptotically optimal. This condition implies that any sequence of asymptotically optimal almost-regular quantizers must converge to a uniform quantizer as the distortion tends to zero. While the obtained lower bound itself is not novel, to the best of our knowledge, we present the first rigorous derivation that follows the direct approach by Gish and Pierce without resorting to heuristic high-resolution approximations commonly found in the quantization literature. Furthermore, our derivation holds for all d-dimensional sources having finite differential entropy and whose integer part has finite entropy. In contrast to Gish and Pierce, we do not require additional constraints on the continuity or decay of the source pdf. ; This work has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement number 714161), from the 7th European Union Framework Programme under Grant 333680, from the Ministerio de Economía y Competitividad of Spain under Grants TEC2013-41718-R, RYC-2014-16332, IJCI-2015-27020, TEC2015-69648-REDC, and TEC2016-78434-C3-3-R (AEI/FEDER, EU), and from the Comunidad de Madrid under Grant S2103/ICE-2845. The material in this paper was presented in part at the 2016 IEEE International Symposium on Information Theory, Barcelona, Spain, July 2016.