Noisy Channel-Output Feedback Capacity of the Linear Deterministic Interference Channel

In this paper, the capacity region of the two-user linear deterministic (LD) interference channel with noisy output feedback (IC-NOF) is fully characterized. This result allows the identification of several asymmetric scenarios in which imple- menting channel-output feedback in only one of the transmitter- receiver pairs is as beneficial as implementing it in both links, in terms of achievable individual rate and sum-rate improvements w.r.t. the case without feedback. In other scenarios, the use of channel-output feedback in any of the transmitter-receiver pairs benefits only one of the two pairs in terms of achievable individual rate improvements or simply, it turns out to be useless, i.e., the capacity regions with and without feedback turn out to be identical even in the full absence of noise in the feedback links.Comment: 5 pages, 9 figures, see proofs in V. Quintero, S. M. Perlaza, and J.-M. Gorce, "Noisy channel-output feedback capacity of the linear deterministic interference channel," INRIA, Tech. Rep. 456, Jan. 2015. This was submitted and accepted in IEEE ITW 201

Nash Region of the Linear Deterministic Interference Channel with Noisy Output Feedback

In this paper, the $\eta$-Nash equilibrium ($\eta$-NE) region of the two-user linear deterministic interference channel (IC) with noisy channel-output feedback is characterized for all $\eta > 0$. The $\eta$-NE region, a subset of the capacity region, contains the set of all achievable information rate pairs that are stable in the sense of an $\eta$-NE. More specifically, given an $\eta$-NE coding scheme, there does not exist an alternative coding scheme for either transmitter-receiver pair that increases the individual rate by more than $\eta$ bits per channel use. Existing results such as the $\eta$-NE region of the linear deterministic IC without feedback and with perfect output feedback are obtained as particular cases of the result presented in this paper.Comment: 5 pages, 2 figures, to appear in ISIT 201

Joint constraints on reionization: a framework for combining the global 21cm signal and the kinetic Sunyaev-Zel'dovich effect

Recent measurements from the CMB and from high-redshift galaxy observations have placed rough constraints on the midpoint and duration of the Epoch of Reionization. Detailed measurements of the ionization history remain elusive, although two proposed probes show great promise for this purpose: the 21cm global signal and the kinetic Sunyaev-Zel'dovich (kSZ) effect. We formally confirm the common assumption that these two probes are highly complementary, with the kSZ being more sensitive to extended ionization histories and the global signal to rapidly evolving ones. We do so by performing a Karhunen-Lo\`{e}ve (KL) transformation, which casts the data in a basis designed to emphasize the information content of each probe. We find that reconstructing the ionization history using both probes gives significantly more precise results than individual constraints, although carefully chosen, physically motivated priors play a crucial part in obtaining a bias-free reconstruction. Additionally, in the KL basis, measurements from one probe can be used to detect the presence of residual systematics in the other, providing a safeguard against systematics that would go undetected when data from each probe is analyzed in isolation. Once detected, the modes contaminated by systematics can be discarded from the data analysis to avoid biases in reconstruction

Retrieving cosmological information from small-scale CMB foregrounds. I. The thermal Sunyaev Zel'dovich effect

We propose a new analysis of small-scale cosmic microwave background (CMB) data by introducing the cosmological dependency of the foreground signals, focussing first on the thermal Sunyaev-Zel’dovich (tSZ) power spectrum, derived from the halo model. We analyse the latest observations by the South Pole Telescope (SPT) of the high-ℓ power (cross) spectra at 95, 150, and 220 GHz, as the sum of CMB and tSZ signals, both depending on cosmological parameters and remaining contaminants. In order to perform faster analyses, we propose a new tSZ modelling based on machine learning algorithms (namely Random Forest). We show that the additional information contained in the tSZ power spectrum tightens constraints on cosmological and tSZ scaling relation parameters. We combined for the first time the Planck tSZ data with SPT high-ℓ to derive new constraints. Finally, we show how the amplitude of the remaining kinetic SZ power spectrum varies depending on the assumptions made on both tSZ and cosmological parameters. These results show the importance of a thorough modelling of foregrounds in the cosmological analysis of small-scale CMB data. Reliable constraints on cosmological parameters can only be achieved once other significant foregrounds, such as the kinetic SZ and the cosmic infrared background (CIB), are also properly accounted fo

When Does Output Feedback Enlarge the Capacity of the Interference Channel?

In this paper, the benefits of channel-output feedback in the Gaussian interference channel (G-IC) are studied under the effect of additive Gaussian noise. Using a linear deterministic (LD) model, the signal to noise ratios (SNRs) in the feedback links beyond which feedback plays a significant role in terms of increasing the individual rates or the sum-rate are approximated. The relevance of this work lies on the fact that it identifies the feedback SNRs for which in any G-IC one of the following statements is true: (a) feedback does not enlarge the capacity region; (b) feedback enlarges the capacity region and the sum-rate is greater than the largest sum-rate without feedback; and (c) feedback enlarges the capacity region but no significant improvement is observed in the sum-rate

Observational constraints on key-parameters of cosmic reionisation history

We discuss constraints on cosmic reionisation and their implications on a cosmic star formation rate (SFR) density ρSFR model; we study the influence of key-parameters such as the clumping factor of ionised hydrogen in the intergalactic medium (IGM) CH II and the fraction of ionising photons escaping star-forming galaxies to reionise the IGM fesc. Our analysis has used SFR history data from luminosity functions, assuming that star-forming galaxies were sufficient to lead the reionisation process at high redshift. We have added two other sets of constraints: measurements of the IGM ionised fraction and the most recent result from Planck Satellite about the integrated Thomson optical depth of the cosmic microwave background τPlanck. Our analysis shows that a reionisation beginning as early as z ≥ 14 and persisting until z ∼ 6 is a likely scenario. We also considered various possibilities for the evolution of fesc and CHII withredshift,andconfrontthemwithobservationaldatacitedabove.Weconcludethat,ifthemodelofaconstantclumpingfactor is chosen, the fiducial value of three is consistent with observations; even if a redshift-dependent model is considered, the resulting opticaldepthisstronglycorrelatedwithCHII meanvalueatz>7,anadditionalargumentinfavouroftheuseofaconstantclumping factor. Similarly, a constant value of the escape fraction is favoured over a redshift-dependent model. When added as a fit parameter, we find fesc = 0.19 ± 0.04. However, this result strongly depends on the choice of magnitude limit in the derivation of ρSFR. Our fiducial analysis considers faint galaxies (Mlim = −13) and the result is a well constrained escape fraction of about 0.2, but when Mlim = −17, the number of galaxies available to reionise the IGM is not sufficient to match the observations, so that much higher values of fesc, approaching 70%, are needed

Impact of survey geometry and super-sample covariance on future photometric galaxy surveys

Photometric galaxy surveys probe the late-time Universe where the density field is highly non-Gaussian. A consequence is the emergence of the super-sample covariance (SSC), a non-Gaussian covariance term that is sensitive to fluctuations on scales larger than the survey window. In this work, we study the impact of the survey geometry on the SSC and, subsequently, on cosmological parameter inference. We devise a fast SSC approximation that accounts for the survey geometry and compare its performance to the common approximation of rescaling the results by the fraction of the sky covered by the survey, fSKY, dubbed ‘full-sky approximation’. To gauge the impact of our new SSC recipe, that we call ‘partial-sky’, we perform Fisher forecasts on the parameters of the (w0, wa)-CDM model in a 3 × 2 point analysis, varying the survey area, the geometry of the mask, and the galaxy distribution inside our redshift bins. The differences in the marginalised forecast errors –with the full-sky approximation performing poorly for small survey areas but excellently for stage-IV-like areas– are found to be absorbed by the marginalisation on galaxy bias nuisance parameters. For large survey areas, the unmarginalised errors are underestimated by about 10% for all probes considered. This is a hint that, even for stage-IV-like surveys, the partial-sky method introduced in this work will be necessary if tight priors are applied on these nuisance parameters. We make the partial-sky method public with a new release of the public code PySSC

The failed liberalisation of Algeria and the international context: a legacy of stable authoritarianism

The paper attempts to challenge the somewhat marginal role of international factors in the study of transitions to democracy. Theoretical and practical difficulties in proving causal mechanisms between international variables and domestic outcomes can be overcome by defining the international dimension in terms of Western dominance of world politics and by identifying Western actions towards democratising countries. The paper focuses on the case of Algeria, where international factors are key in explaining the initial process of democratisation and its following demise. In particular, the paper argues that direct Western policies, the pressures of the international system and external shocks influence the internal distribution of power and resources, which underpins the different strategies of all domestic actors. The paper concludes that analysis based purely on domestic factors cannot explain the process of democratisation and that international variables must be taken into more serious account and much more detailed

Capacité du canal linéaire déterministe à interférences avec voies de retour bruitées

International audienceIn this article, the capacity region of the two-user linear deterministic (LD) interference channel with noisy output feedback (IC-NOF) is fully characterized. This result allows the identification of several asymmetric scenarios in which implementing channel-output feedback in only one of the transmitter-receiver pairs is as beneficial as implementing it in both links, in terms of achievable individual rate and sum-rate improvements w.r.t. the case without feedback. In other scenarios, the use of channel-output feedback in any of the transmitter-receiver pairs benefits only one of the two pairs in terms of achievable individual rate improvements or simply, it turns out to be useless, i.e., the capacity regions with and without feedback turn out to be identical even in the full absence of noise in the feedback links.Cet article présente la caractérisation de la région de capacité du canal linéaire déterministè a interférences avec voies de retour degradées entre chaque pairé emetteur-récepteur. L'apport de ce travail porte sur l'ajout de voies de retour bruitées et sur l'´ etude de scénarios asymétriques. Nous etudions quelques scénarios types et montrons que dans certains cas, l'utilisation d'une seule des voies de retour permet d'obtenir le même gain qu'avec les deux voies. Ce gain par rapport au canal sans voie de retour est mis en evidence par l' amélioration des taux de transmission individuels et de leur somme. D'autres scénarios montrent qu'une seule voie de retour améliore le taux individuel d'un des deux couples emetteur-récepteur seulement. Il existe enfin d'autres scenarios pour lesquels les voies de retour n'apportent aucun gain ni pour les taux individuels ni pour leur somme. Dans ces scenarios, cela montre que les régions de capacité avec et sans voie de retour sont identiques