Maël Le Treust

Spectrum sharing games on the interference channel

In this paper, we address the problem of spectrum sharing where competitive operators coexist in the same frequency band. First, we model this problem as a strategic non-cooperative game where operators simultaneously share the spectrum according to the Nash Equilibrium (N.E). Given a set of channel realizations, several Nash equilibria exist which renders the outcome of the game unpredictable. For this reason, the spectrum sharing problem is reformulated as a Stackelberg game where the first operator is already being deployed and the secondary operator follows next. The Stackelberg equilibrium (S.E) is reached where the best response of the secondary operator is taken into account upon maximizing the primary operators utility function. Finally, we assess the goodness of the proposed distributed approach by comparing its performance to the centralized approach.

Green Power Control in Cognitive Wireless Networks

A decentralized network of cognitive and noncognitive transmitters where each transmitter aims at maximizing his energy efficiency is considered. The cognitive transmitters are assumed to be able to sense the transmit power of their noncognitive counterparts and the former have a cost for sensing. The Stackelberg equilibrium analysis of this two-level hierarchical game is conducted, which allows us to better understand the effects of cognition on energy efficiency. In particular, it is proven that the network energy efficiency is maximized when only a given fraction of terminals are cognitive. Then, we study a sensing game where all the transmitters are assumed to take the decision of whether to sense (namely to be cognitive) or not. This game is shown to be a weighted potential game, and its set of equilibria is studied. Playing the sensing game in a first phase (e.g., of a time slot) and then playing the power control game is shown to be more efficient individually for all transmitters than playing a game where a transmitter would jointly optimize whether to sense his power level, showing the existence of a kind of Braess paradox. The derived results are illustrated by numerical results and provide some insights on how to deploy cognitive radios in heterogeneous networks in terms of sensing capabilities.

An achievable rate region for the broadcast wiretap channel with asymmetric side information

The communication scenario under consideration in this paper corresponds to a multiuser channel with side information and consists of a broadcast channel with two legitimate receivers and an eavesdropper. Mainly, the results obtained are as follows. First, an achievable rate region is provided for the (general) case of discrete-input discrete-output channels, generalizing existing results. Second, the obtained theorem is used to derive achievable transmission rates for two practical cases of Gaussian channels. It is shown that known perturbations can enlarge the rate region of broadcast wiretap channels with side information and having side information at the decoder as well can increase the secrecy rate of channels with side information. Third, we establish for the first time an explicit connection between multiuser channels and observation structures in dynamic games. In this respect, we show how to exploit the proved achievability theorem (discrete case) to derive a communication-compatible upper bound on the minmax level of a player.

Correlation between channel state and information source with empirical coordination constraint

Correlation between channel state and source symbol is under investigation for a joint source-channel coding problem. We investigate simultaneously the lossless transmission of information and the empirical coordination of channel inputs with the symbols of source and states. Empirical coordination is achievable if the sequences of source symbols, channel states, channel inputs and channel outputs are jointly typical for a target joint probability distribution. We characterize the joint distributions that are achievable under lossless decoding constraint. The performance of the coordination is evaluated by an objective function. For example, we determine the minimal distortion between symbols of source and channel inputs for lossless decoding. We show that the correlation source/channel state improves the feasibility of the transmission.

Empirical coordination with two-sided state information and correlated source and state

The coordination of autonomous agents is a critical issue for decentralized communication networks. Instead of transmitting information, the agents interact in a coordinated manner in order to optimize a general objective function. A target joint probability distribution is achievable if there exists a code such that the sequences of symbols are jointly typical. The empirical coordination is strongly related to the joint source-channel coding with two-sided state information and correlated source and state. This problem is also connected to state communication and is open for non-causal encoder and decoder. We characterize the optimal solutions for perfect channel, for lossless decoding, for independent source and channel, for causal encoding and for causal decoding.

Polar coding for empirical coordination of signals and actions over noisy channels

We develop a polar coding scheme for empirical coordination in a two-node network with a noisy link in which the input and output signals have to be coordinated with the source and the reconstruction. In the case of non-causal encoding and decoding, we show that polar codes achieve the best known inner bound for the empirical coordination region, provided that a vanishing rate of common randomness is available. This scheme provides a constructive alternative to random binning and coding proofs.

Information design for strategic coordination of autonomous devices with non-aligned utilities

In this paper, we investigate the coordination of autonomous devices with non-aligned utility functions. Both encoder and decoder are considered as players, that choose the encoding and the decoding in order to maximize their long-run utility functions. The topology of the point-to-point network under investigation, suggests that the decoder implements a strategy, knowing in advance the strategy of the encoder. We characterize the encoding and decoding functions that form an equilibrium, by using empirical coordination. The equilibrium solution is related to an auxiliary game in which both players choose some conditional distributions in order to maximize their expected utilities. This problem is closely related to the literature on “Information Design” in Game Theory. We also characterize the set of posterior distributions that are compatible with a rate-limited channel between the encoder and the decoder. Finally, we provide an example of non-aligned utility functions corresponding to parallel fading multiple access channels.

Empirical coordination with channel feedback and strictly causal or causal encoding

In multi-terminal networks, feedback increases the capacity region and helps communication devices to coordinate. In this article, we deepen the relationship between coordination and feedback by considering a point-to-point scenario with an information source and a noisy channel. Empirical coordination is achievable if the encoder and the decoder can implement sequences of symbols that are jointly typical for a target probability distribution. We investigate the impact of feedback when the encoder has strictly causal or causal observation of the source symbols. For both cases, we characterize the optimal information constraints and we show that feedback improves coordination possibilities. Surprisingly, feedback also reduces the number of auxiliary random variables and simplifies the information constraints. For empirical coordination with strictly causal encoding and feedback, the information constraint does not involve auxiliary random variable anymore.

Secrecy & Rate Adaptation for secure HARQ protocols

This paper is dedicated to the study of HARQ protocols under a secrecy constraint. An encoder sends information to a legitimate decoder while keeping it secret from the eavesdropper. Our objective is to provide a coding scheme that satisfies both reliability and confidentiality conditions. This problem has been investigated in the literature using a coding scheme that involves a unique secrecy parameter. The uniqueness of this parameter is sub-optimal for the throughput criteria and we propose a new coding scheme that introduces additional degrees of freedom. Our code involves Secrecy Adaptation and Rate Adaptation and we called it SARA-code. The first contribution is to prove that the SARA-code has small error probability and small information leakage rate. The second contribution is to show, over a numerical example, that the SARA-code improves the secrecy throughput.

On the benefits of repeated game models for green cross-layer power control in small cells

In this paper, we consider the problem of distributed power control for multiple access channels when energy-efficiency has to be optimized. In contrast with related works, the presence of a queue at each transmitter is accounted for and globally efficient solutions are sought. To this end, a repeated game model is exploited and shown to lead to solutions which are distributed in the sense of the decision, perform well globally, and may rely on limited channel state information at the transmitter.