Approximate Capacity Region of the Two-User Gaussian Interference Channel with Noisy Channel-Output Feedback

In this paper, the capacity region of the linear deterministic interference channel with noisy channel-output feedback (LD-IC-NF) is fully characterized. The proof of achievability is based on random coding arguments and rate splitting; blockMarkov superposition coding; and backward decoding. The proof of converse reuses some of the existing outer bounds and includes new ones obtained using genie-aided models. Following the insight gained from the analysis of the LD-IC-NF, an achievability region and a converse region for the two-user Gaussian interference channel with noisy channel-output feedback (GIC-NF) are presented. Finally, the achievability region and the converse region are proven to approximate the capacity region of the G-IC-NF to within 4.4 bits

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

Approximate Nash Region of the Gaussian Interference Channel with Noisy Output Feedback

International audienceIn this paper, an achievable $\eta$-Nash equilibrium ($\eta$-NE) region for the two-user Gaussian interference channel with noisy channel-output feedback is presented for all $\eta \geqslant 1$. This result is obtained in the scenario in which each transmitter-receiver pair chooses its own transmit-receive configuration in order to maximize its own individual information transmission rate. At an $\eta$-NE, any unilateral deviation by either of the pairs does not increase the corresponding individual rate by more than $\eta$ bits per channel use

On the Efficiency of Nash Equilibria in the Interference Channel with Noisy Feedback

International audienceIn this paper, the price of anarchy (PoA) and the price of stability (PoS) of the η-Nash equilibrium (η-NE), of the two-user linear deterministic interference channel with noisy channel-output feedback are characterized, with η > 0 arbitrarily small. The price of anarchy is the ratio between the sum-rate capacity and the smallest sum-rate at an η-NE. The price of stability is the ratio between the sum-rate capacity and the biggest sum-rate at an η-NE. Some of the main conclusions of this work are the following: (a) When both transmitter-receiver pairs are in low interference regime, the PoA can be made arbitrarily close to one as η approaches zero, subject to a particular condition. More specifically, there are scenarios in which even the worst η-NE (in terms of sum-rate) is arbitrarily close to the Pareto boundary of the capacity region. (b) The use of feedback plays a fundamental role on increasing the PoA, in some interference regimes. This is basically because in these regimes, the use of feedback increases the sum-capacity, whereas the smallest sum-rate at an η-NE remains the same. (c) The PoS is equal to one in all interference regimes. This implies that there always exists an η-NE in the Pareto boundary of the capacity region. The ensemble of conclusions of this work reveal the relevance of jointly using equilibrium selection methods and channel-output feedback for reducing the effect of anarchical behavior of the network components in the η-NE sum-rate of the interference channel

Simultaneous Information and Energy Transmission in the Two-User Gaussian Interference Channel

International audienceIn this paper, the fundamental limits of simultaneous information and energy transmission (SIET) in the two-user Gaussian interference channel (G-IC) with and without perfect channel-output feedback are approximated by two regions in each case, i.e., an achievable region and a converse region. When the energy transmission rate is normalized by the maximum energy rate, the approximation is within a constat gap. In the proof of achievability, the key idea is the use of power-splitting between two signal components: an information-carrying component and a no-information component. The construction of the former is based on random coding arguments, whereas the latter consists in a deterministic sequence known by all transmitters and receivers. The proof of the converse is obtained via cut-set bounds, genie-aided channel models, Fano's inequality and some concentration inequalities considering that channel inputs might have a positive mean. Finally, the energy transmission enhancement due to feedback is quantified and it is shown that feedback can at most double the energy transmission rate at high signal to noise ratios

Quand est-ce que la rétro-alimentation améliore la region de capacité du canal à interférences?

In this research report, 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 higher than the largest sum-rate without feedback; and (c) Feedback enlarges the capacity region but no significant improvement is observed in the sum-rate.Dans ce rapport, l’impact du bruit additif sur les liens de rétro-alimentation dans le canal Gaussien à interférences est étudié en utilisant des approximations linéaires déterministes. Sous ces hypothèses, la valeur exacte du rapport signal à bruit (RSB) sur le lien de rétro- alimentation, au-delà de laquelle l’approximation linéaire déterministe de la région de capacité est améliorée, est caractérisée en fonction des RSB et des rapports interférences sur bruit (RIB). En général, trois scénarios peuvent être observés selon les valeurs exactes des RSB sur les liens directs et des RIBs: (a) L’utilisation de la rétro-alimentation est inutile pour améliorer la région de capacité; (b) L’utilisation de la rétro-alimentation améliore la région de capacité et la somme des taux de transmission; et (c) L’utilisation de la rétro-alimentation améliore la région de capacité mais la somme des taux de transmission n’est pas ameliorée

Canal à interférences décentralisé avec rétroalimentation dégradée

In this research report, the $\eta$-Nash equilibrium ($\eta$-NE) region of the two-user linear deterministic interference channel with noisy channel-output feedback is characterized for all $\eta > 0$ arbitrarily small. It also characterizes the $\eta$-Nash achievable region of the two-user Gaussian interference with noisy channel output feedback for all $\eta > 1$. 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 interference channel and the Gaussian interference channel without feedback and with perfect output feedback are obtained as particular cases of the result presented in this research report.Ce rapport de recherche présente la région d’ équilibre $\eta$-Nash ($\eta$-Nash) du canal linéaire déterministe à interférences avec rétroalimentation dégradée par bruit additif pour tout $\eta > 0$ arbitrairement petits. Il caractérise également la région d’ équilibre $\eta$-Nash atteignable du canal Gaussien à interférences avec rétroalimentation dégradée par bruit additif pour tout $\eta > 1$. La région d’ équilibre $\eta$-Nash, un sous-ensemble de la région de capacité, contient l’ensemble de toutes les paires de taux d’information réalisables qui sont stables au sens d’un $\eta$-NE. Plus précisément, étant donné un schéma de codage $\eta$-NE, il n’existe pas de schéma de codage alternatif poor l’une ou l’autre paire émetteur-récepteur qui augmente le taux individuel de plus de $\eta$ bits par utilisation du canal. Les résultats existants, tels que la région d’ équilibre $\eta$-NE du canal linéaire déterministe à interférences et du canal Gaussien à interférences sans rétroalimentation et avec rétroalimentation parfaite, sont obtenus comme cas particuliers du résultat présenté dans ce rapport de recherche