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

The Nash equilibrium region of the linear deterministic interference channel with feedback

International audienceThe two-user linear deterministic interference channel (LD-IC) with feedback is studied under the assumption that each transmitter aims to selfishly maximize its individual achievable rate by tuning its own transmit configuration. More specifically, each transmitter autonomously tunes parameters such as the number of information bits per block, block length, codebook and encoding/decoding functions. To this end, the Nash equilibrium (NE) region of the LD-IC with feedback is fully characterized. The main observations presented in this paper are: (i) The NE region with feedback is strictly larger than the NE region with no feedback. Moreover, all the new rate pairs achieved with feedback are either strictly Pareto or weakly Pareto optimal. (ii) The use of feedback allows the achievability of all Pareto optimal rate pairs of the capacity region of the LD-IC with feedback

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

Symmetric Decentralized Interference Channels with Noisy Feedback

International audienceIn this paper, all the rate-pairs that are achievable at a Nash equilibrium (NE) in the two-user linear deterministic symmetric decentralized interference channel (LD-S-DIC) with noisy feedback are identified. More specifically, the Nash region (NR) of the LD-S-DIC with noisy feedback is fully characterized. The relevance of these rate-pairs is that once they are achieved by using NE transmit-receive configurations, none of the transmitter-receiver pairs can increase their individual rates by unilaterally changing their configurations. More importantly, it is shown that the NR of the LD-S-DIC with noisy feedback is larger than the NR of the LD-S-DIC without feedback only in certain cases. When interference is stronger than the desired signals, a larger NR is observed only if the signal to noise ratios (SNRs) of the feedback links are higher than the SNRs of the direct links. Conversely, when desired signals are stronger than interference, a larger NR is observed only if the SNRs of the feedback links are higher than both the signal to interference ratios (SIRs) and the interference to noise ratios (INRs) of the direct links. Previous results, namely the NE region of the two-user LD-S-DIC without feedback and with perfect output feedback are obtained as special cases of the results presented in this contribution

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

Perfect Output Feedback in the Two-User Decentralized Interference Channel

In this paper, the $\eta$-Nash equilibrium ($\eta$-NE) region of the two-user Gaussian interference channel (IC) with perfect output feedback is approximated to within $1$ bit/s/Hz and $\eta$ arbitrarily close to $1$ bit/s/Hz. The relevance of the $\eta$-NE region is that it provides the set of rate-pairs that are achievable and stable in the IC when both transmitter-receiver pairs autonomously tune their own transmit-receive configurations seeking an $\eta$-optimal individual transmission rate. Therefore, any rate tuple outside the $\eta$-NE region is not stable as there always exists one link able to increase by at least $\eta$ bits/s/Hz its own transmission rate by updating its own transmit-receive configuration. The main insights that arise from this work are: $(i)$ The $\eta$-NE region achieved with feedback is larger than or equal to the $\eta$-NE region without feedback. More importantly, for each rate pair achievable at an $\eta$-NE without feedback, there exists at least one rate pair achievable at an $\eta$-NE with feedback that is weakly Pareto superior. $(ii)$ There always exists an $\eta$-NE transmit-receive configuration that achieves a rate pair that is at most $1$ bit/s/Hz per user away from the outer bound of the capacity region.Comment: Revised version (Aug. 2015

Joint Scheduling and ARQ for MU-MIMO Downlink in the Presence of Inter-Cell Interference

User scheduling and multiuser multi-antenna (MU-MIMO) transmission are at the core of high rate data-oriented downlink schemes of the next-generation of cellular systems (e.g., LTE-Advanced). Scheduling selects groups of users according to their channels vector directions and SINR levels. However, when scheduling is applied independently in each cell, the inter-cell interference (ICI) power at each user receiver is not known in advance since it changes at each new scheduling slot depending on the scheduling decisions of all interfering base stations. In order to cope with this uncertainty, we consider the joint operation of scheduling, MU-MIMO beamforming and Automatic Repeat reQuest (ARQ). We develop a game-theoretic framework for this problem and build on stochastic optimization techniques in order to find optimal scheduling and ARQ schemes. Particularizing our framework to the case of "outage service rates", we obtain a scheme based on adaptive variable-rate coding at the physical layer, combined with ARQ at the Logical Link Control (ARQ-LLC). Then, we present a novel scheme based on incremental redundancy Hybrid ARQ (HARQ) that is able to achieve a throughput performance arbitrarily close to the "genie-aided service rates", with no need for a genie that provides non-causally the ICI power levels. The novel HARQ scheme is both easier to implement and superior in performance with respect to the conventional combination of adaptive variable-rate coding and ARQ-LLC.Comment: Submitted to IEEE Transactions on Communications, v2: small correction

Distributive Power Control Algorithm for Multicarrier Interference Network over Time-Varying Fading Channels - Tracking Performance Analysis and Optimization

Distributed power control over interference limited network has received an increasing intensity of interest over the past few years. Distributed solutions (like the iterative water-filling, gradient projection, etc.) have been intensively investigated under \emph{quasi-static} channels. However, as such distributed solutions involve iterative updating and explicit message passing, it is unrealistic to assume that the wireless channel remains unchanged during the iterations. Unfortunately, the behavior of those distributed solutions under \emph{time-varying} channels is in general unknown. In this paper, we shall investigate the distributed scaled gradient projection algorithm (DSGPA) in a $K$ pairs multicarrier interference network under a finite-state Markov channel (FSMC) model. We shall analyze the \emph{convergence property} as well as \emph{tracking performance} of the proposed DSGPA. Our analysis shows that the proposed DSGPA converges to a limit region rather than a single point under the FSMC model. We also show that the order of growth of the tracking errors is given by \mathcal{O}\(1 \big/ \bar{N}\), where $\bar{N}$ is the \emph{average sojourn time} of the FSMC. Based on the analysis, we shall derive the \emph{tracking error optimal scaling matrices} via Markov decision process modeling. We shall show that the tracking error optimal scaling matrices can be implemented distributively at each transmitter. The numerical results show the superior performance of the proposed DSGPA over three baseline schemes, such as the gradient projection algorithm with a constant stepsize.Comment: To Appear on the IEEE Transaction on Signal Processin

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