arXiv subjects

Achilleas Anastasopoulos

Publications and source records attributed to Achilleas Anastasopoulos.

33 records · Page 2Linked to original sources

arXiv2017

Variable-length codes for channels with memory and feedback: error-exponent upper bounds

The reliability function of memoryless channels with noiseless feedback and variable-length coding has been found to be a linear function of the average rate in the classic work of Burnashev. In this work we consider unifilar channels with noiseless feedback and study upper bounds for the channel reliability function with variable length codes. In unifilar channels the channel state is known to the transmitter but is unknown to the receiver. We generalize Burnashev's analysis and derive a similar expression which is linear in average rate and depends on the channel capacity, as well as an additional parameter which relates to a sequential binary hypothesis testing problem over this channel. This parameter is evaluated by setting up an appropriate Markov decision process (MDP). Furthermore, an upper bound for this parameter is derived using a simplified MDP. Numerical evaluation of the parameter for several binary input/state/output unifilar channels hints at the optimal transmission strategies. Such strategies are studied in a companion paper to provide lower (achievable) bounds on the channel reliability function.

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arXiv2017

Distributed Mechanism Design with Learning Guarantees

Mechanism design for fully strategic agents commonly assumes broadcast nature of communication between agents of the system. Moreover, for mechanism design, the stability of Nash equilibrium (NE) is demonstrated by showing convergence of specific pre-designed learning dynamics, rather than for a class of learning dynamics. In this paper we consider two common resource allocation problems: sharing $ K $ infinitely divisible resources among strategic agents for their private consumption (private goods), and determining the level for an infinitely divisible public good with $ P $ features, that is shared between strategic agents. For both cases, we present a distributed mechanism for a set of agents who communicate through a given network. In a distributed mechanism, agents' messages are not broadcast to all other agents as in the standard mechanism design framework, but are exchanged only in the local neighborhood of each agent. The presented mechanisms produce a unique NE and fully implement the social welfare maximizing allocation. In addition, the mechanisms are budget-balanced at NE. It is also shown that the mechanisms induce a game with contractive best-response, leading to guaranteed convergence for all learning dynamics within the Adaptive Best-Response dynamics class, including dynamics such as Cournot best-response, $ k- $period best-response and Fictitious Play. We also present a numerically study of convergence under repeated play, for various communication graphs and learning dynamics.

cs.GT↗

arXiv2017

Mechanism design for resource allocation in networks with intergroup competition and intragroup sharing

We consider a network where strategic agents, who are contesting for allocation of resources, are divided into fixed groups. The network control protocol is such that within each group agents get to share the resource and across groups they contest for it. A prototypical example is the allocation of data rate on a network with multicast/multirate architecture. Compared to the unicast architecture (which is a special case), the multicast/multirate architecture can result in substantial bandwidth savings. However, design of a market mechanism in such a scenario requires dealing with both private and public good problems as opposed to just private goods in unicast. The mechanism proposed in this work ensures that social welfare maximizing allocation on such a network is realized at all Nash equilibria (NE) i.e., full implementation in NE. In addition it is individually rational, i.e., agents have an incentive to participate in the mechanism. The mechanism, which is constructed in a quasi-systematic way starting from the dual of the centralized problem, has a number of useful properties. Specifically, due to a novel allocation scheme, namely "radial projection", the proposed mechanism results in feasible allocation even off equilibrium. This is a practical necessity for any realistic mechanism since agents have to "learn" the NE through a dynamic process. Finally, it is shown how strong budget balance at equilibrium can be achieved with a minimal increase in message space as an add-on to a weakly budget balanced mechanism.

cs.GT↗

arXiv2016

Structured Perfect Bayesian Equilibrium in Infinite Horizon Dynamic Games with Asymmetric Information

In dynamic games with asymmetric information structure, the widely used concept of equilibrium is perfect Bayesian equilibrium (PBE). This is expressed as a strategy and belief pair that simultaneously satisfy sequential rationality and belief consistency. Unlike symmetric information dynamic games, where subgame perfect equilibrium (SPE) is the natural equilibrium concept, to date there does not exist a universal algorithm that decouples the interdependence of strategies and beliefs over time in calculating PBE. In this paper we find a subset of PBE for an infinite horizon discounted reward asymmetric information dynamic game. We refer to it as Structured PBE or SPBE; in SPBE, any agents' strategy depends on the public history only through a common public belief and on private history only through the respective agents' latest private information (his private type). The public belief acts as a summary of all the relevant past information and it's dimension does not increase with time. The motivation for this comes the common information approach proposed in Nayyar et al. (2013) for solving decentralized team (non-strategic) resource allocation problems with asymmetric information. We calculate SPBE by solving a single-shot fixed-point equation and a corresponding forward recursive algorithm. We demonstrate our methodology by means of a public goods example.

cs.GT↗

arXiv2016

Signaling equilibria for dynamic LQG games with asymmetric information

We consider a finite horizon dynamic game with two players who observe their types privately and take actions, which are publicly observed. Players' types evolve as independent, controlled linear Gaussian processes and players incur quadratic instantaneous costs. This forms a dynamic linear quadratic Gaussian (LQG) game with asymmetric information. We show that under certain conditions, players' strategies that are linear in their private types, together with Gaussian beliefs form a perfect Bayesian equilibrium (PBE) of the game. Furthermore, it is shown that this is a signaling equilibrium due to the fact that future beliefs on players' types are affected by the equilibrium strategies. We provide a backward-forward algorithm to find the PBE. Each step of the backward algorithm reduces to solving an algebraic matrix equation for every possible realization of the state estimate covariance matrix. The forward algorithm consists of Kalman filter recursions, where state estimate covariance matrices depend on equilibrium strategies.

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arXiv2015

Mechanism Design for Fair Allocation

Mechanism design for a social utility being the sum of agents' utilities (SoU) is a well-studied problem. There are, however, a number of problems of theoretical and practical interest where a designer may have a different objective than maximization of the SoU. One motivation for this is the desire for more equitable allocation of resources among agents. A second, more subtle, motivation is the fact that a fairer allocation indirectly implies less variation in taxes which can be desirable in a situation where (implicit) individual agent budgetary constraints make payment of large taxes unrealistic. In this paper we study a family of social utilities that provide fair allocation (with SoU being subsumed as an extreme case) and derive conditions under which Bayesian and Dominant strategy implementation is possible. Furthermore, it is shown how a simple modification of the above mechanism can guarantee full Bayesian implementation. Through a numerical example it is shown that the proposed method can result in significant gains both in allocation fairness and tax reduction.

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arXiv2015

A General Mechanism Design Methodology for Social Utility Maximization with Linear Constraints

Social utility maximization refers to the process of allocating resources in such a way that the sum of agents' utilities is maximized under the system constraints. Such allocation arises in several problems in the general area of communications, including unicast (and multicast multi-rate) service on the Internet, as well as in applications with (local) public goods, such as power allocation in wireless networks, spectrum allocation, etc. Mechanisms that implement such allocations in Nash equilibrium have also been studied but either they do not possess full implementation property, or are given in a case-by-case fashion, thus obscuring fundamental understanding of these problems. In this paper we propose a unified methodology for creating mechanisms that fully implement, in Nash equilibria, social utility maximizing functions arising in various contexts where the constraints are convex. The construction of the mechanism is done in a systematic way by considering the dual optimization problem. In addition to the required properties of efficiency and individual rationality that such mechanisms ought to satisfy, three additional design goals are the focus of this paper: a) the size of the message space scaling linearly with the number of agents (even if agents' types are entire valuation functions), b) allocation being feasible on and off equilibrium, and c) strong budget balance at equilibrium and also off equilibrium whenever demand is feasible.

cs.GT↗

arXiv2014

Generalized Proportional Allocation Mechanism Design for Unicast Service on the Internet

In this report we construct two mechanisms that fully implement social welfare maximising allocation in Nash equilibria for the case of a single infinitely divisible good subject to multiple inequality constraints. The first mechanism achieves weak budget balance, while the second is an extension of the first, and achieves strong budget balance. One important application of this mechanism is unicast service on the Internet where a network operator wishes to allocate rates among strategic users in such a way that maximise overall user satisfaction while respecting capacity constraints on every link in the network. The emphasis of this work is on full implementation, which means that all Nash equilibria of the induced game result in the optimal allocations of the centralized allocation problem.

cs.GT↗

arXiv2010

Typicality Graphs:Large Deviation Analysis

Let $\mathcal{X}$ and $\mathcal{Y}$ be finite alphabets and $P_{XY}$ a joint distribution over them, with $P_X$ and $P_Y$ representing the marginals. For any $ε> 0$, the set of $n$-length sequences $x^n$ and $y^n$ that are jointly typical \cite{ckbook} according to $P_{XY}$ can be represented on a bipartite graph. We present a formal definition of such a graph, known as a \emph{typicality} graph, and study some of its properties.

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arXiv2010

Error Exponent for Multiple-Access Channels:Lower Bounds

A unified framework to obtain all known lower bounds (random coding, typical random coding and expurgated bound) on the reliability function of a point-to-point discrete memoryless channel (DMC) is presented. By using a similar idea for a two-user discrete memoryless (DM) multiple-access channel (MAC), three lower bounds on the reliability function are derived. The first one (random coding) is identical to the best known lower bound on the reliability function of DM-MAC. It is shown that the random coding bound is the performance of the average code in the constant composition code ensemble. The second bound (Typical random coding) is the typical performance of the constant composition code ensemble. To derive the third bound (expurgated), we eliminate some of the codewords from the codebook with larger rate. This is the first bound of this type that explicitly uses the method of expurgation for MACs. It is shown that the exponent of the typical random coding and the expurgated bounds are greater than or equal to the exponent of the known random coding bounds for all rate pairs. Moreover, an example is given where the exponent of the expurgated bound is strictly larger. All these bounds can be universally obtained for all discrete memoryless MACs with given input and output alphabets.

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arXiv2010

A New Upper Bound on the Average Error Exponent for Multiple-Access Channels

A new lower bound for the average probability or error for a two-user discrete memoryless (DM) multiple-access channel (MAC) is derived. This bound has a structure very similar to the well-known sphere packing packing bound derived by Haroutunian. However, since explicitly imposes independence of the users' input distributions (conditioned on the time-sharing auxiliary variable) results in a tighter sphere-packing exponent in comparison to Haroutunian's. Also, the relationship between average and maximal error probabilities is studied. Finally, by using a known sphere packing bound on the maximal probability of error, a lower bound on the average error probability is derived.

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arXiv2009

A New Universal Random-Coding Bound for Average Probability Error Exponent for Multiple-Access Channels

In this work, a new upper bound for average error probability of a two-user discrete memoryless (DM) multiple-access channel (MAC) is derived. This bound can be universally obtained for all discrete memoryless MACs with given input and output alphabets. This is the first bound of this type that explicitly uses the method of expurgation. It is shown that the exponent of this bound is greater than or equal to those of previously known bounds.

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arXiv2008

A New Sphere-Packing Bound for Maximal Error Exponent for Multiple-Access Channels

In this work, a new lower bound for the maximal error probability of a two-user discrete memoryless (DM) multiple-access channel (MAC) is derived. This is the first bound of this type that explicitly imposes independence of the users' input distributions (conditioned on the time-sharing auxiliary variable) and thus results in a tighter sphere-packing exponent when compared to the tightest known exponent derived by Haroutunian.

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arXiv2006

Iterative Decoding Performance Bounds for LDPC Codes on Noisy Channels

The asymptotic iterative decoding performances of low-density parity-check (LDPC) codes using min-sum (MS) and sum-product (SP) decoding algorithms on memoryless binary-input output-symmetric (MBIOS) channels are analyzed in this paper. For MS decoding, the analysis is done by upper bounding the bit error probability of the root bit of a tree code by the sequence error probability of a subcode of the tree code assuming the transmission of the all-zero codeword. The result is a recursive upper bound on the bit error probability after each iteration. For SP decoding, we derive a recursively determined lower bound on the bit error probability after each iteration. This recursive lower bound recovers the density evolution equation of LDPC codes on the binary erasure channel (BEC) with inequalities satisfied with equalities. A significant implication of this result is that the performance of LDPC codes under SP decoding on the BEC is an upper bound of the performance on all MBIOS channels with the same uncoded bit error probability. All results hold for the more general multi-edge type LDPC codes.

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arXiv2005

Capacity-Achieving Codes with Bounded Graphical Complexity on Noisy Channels

We introduce a new family of concatenated codes with an outer low-density parity-check (LDPC) code and an inner low-density generator matrix (LDGM) code, and prove that these codes can achieve capacity under any memoryless binary-input output-symmetric (MBIOS) channel using maximum-likelihood (ML) decoding with bounded graphical complexity, i.e., the number of edges per information bit in their graphical representation is bounded. In particular, we also show that these codes can achieve capacity on the binary erasure channel (BEC) under belief propagation (BP) decoding with bounded decoding complexity per information bit per iteration for all erasure probabilities in (0, 1). By deriving and analyzing the average weight distribution (AWD) and the corresponding asymptotic growth rate of these codes with a rate-1 inner LDGM code, we also show that these codes achieve the Gilbert-Varshamov bound with asymptotically high probability. This result can be attributed to the presence of the inner rate-1 LDGM code, which is demonstrated to help eliminate high weight codewords in the LDPC code while maintaining a vanishingly small amount of low weight codewords.

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