arXiv subjects

Muriel Medard

Publications and source records attributed to Muriel Medard.

124 records · Page 7Linked to original sources

arXiv2008

Dynamic Rate Allocation in Fading Multiple-access Channels

We consider the problem of rate allocation in a fading Gaussian multiple-access channel (MAC) with fixed transmission powers. Our goal is to maximize a general concave utility function of transmission rates over the throughput capacity region. In contrast to earlier works in this context that propose solutions where a potentially complex optimization problem must be solved in every decision instant, we propose a low-complexity approximate rate allocation policy and analyze the effect of temporal channel variations on its utility performance. To the best of our knowledge, this is the first work that studies the tracking capabilities of an approximate rate allocation scheme under fading channel conditions. We build on an earlier work to present a new rate allocation policy for a fading MAC that implements a low-complexity approximate gradient projection iteration for each channel measurement, and explicitly characterize the effect of the speed of temporal channel variations on the tracking neighborhood of our policy. We further improve our results by proposing an alternative rate allocation policy for which tighter bounds on the size of the tracking neighborhood are derived. These proposed rate allocation policies are computationally efficient in our setting since they implement a single gradient projection iteration per channel measurement and each such iteration relies on approximate projections which has polynomial-complexity in the number of users.

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arXiv2008

Rate and Power Allocation in Fading Multiple Access Channels

We consider the problem of rate and power allocation in a fading multiple-access channel. Our objective is to obtain rate and power allocation policies that maximize a utility function defined over average transmission rates. In contrast with the literature, which focuses on the linear case, we present results for general concave utility functions. We consider two cases. In the first case, we assume that power control is possible and channel statistics are known. In this case, we show that the optimal policies can be obtained greedily by maximizing a linear utility function at each channel state. In the second case, we assume that power control is not possible and channel statistics are not available. In this case, we define a greedy rate allocation policy and provide upper bounds on the performance difference between the optimal and the greedy policy. Our bounds highlight the dependence of the performance difference on the channel variations and the structure of the utility function.

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arXiv2008

Information Theory vs. Queueing Theory for Resource Allocation in Multiple Access Channels

We consider the problem of rate allocation in a fading Gaussian multiple-access channel with fixed transmission powers. The goal is to maximize a general concave utility function of the expected achieved rates of the users. There are different approaches to this problem in the literature. From an information theoretic point of view, rates are allocated only by using the channel state information. The queueing theory approach utilizes the global queue-length information for rate allocation to guarantee throughput optimality as well as maximizing a utility function of the rates. In this work, we make a connection between these two approaches by showing that the information theoretic capacity region of a multiple-access channel and its stability region are equivalent. Moreover, our numerical results show that a simple greedy policy which does not use the queue-length information can outperform queue-length based policies in terms of convergence rate and fairness.

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arXiv2008

On Resource Allocation in Fading Multiple Access Channels - An Efficient Approximate Projection Approach

We consider the problem of rate and power allocation in a multiple-access channel. Our objective is to obtain rate and power allocation policies that maximize a general concave utility function of average transmission rates on the information theoretic capacity region of the multiple-access channel. Our policies does not require queue-length information. We consider several different scenarios. First, we address the utility maximization problem in a nonfading channel to obtain the optimal operating rates, and present an iterative gradient projection algorithm that uses approximate projection. By exploiting the polymatroid structure of the capacity region, we show that the approximate projection can be implemented in time polynomial in the number of users. Second, we consider resource allocation in a fading channel. Optimal rate and power allocation policies are presented for the case that power control is possible and channel statistics are available. For the case that transmission power is fixed and channel statistics are unknown, we propose a greedy rate allocation policy and provide bounds on the performance difference of this policy and the optimal policy in terms of channel variations and structure of the utility function. We present numerical results that demonstrate superior convergence rate performance for the greedy policy compared to queue-length based policies. In order to reduce the computational complexity of the greedy policy, we present approximate rate allocation policies which track the greedy policy within a certain neighborhood that is characterized in terms of the speed of fading.

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arXiv2008

Network coding meets TCP

We propose a mechanism that incorporates network coding into TCP with only minor changes to the protocol stack, thereby allowing incremental deployment. In our scheme, the source transmits random linear combinations of packets currently in the congestion window. At the heart of our scheme is a new interpretation of ACKs - the sink acknowledges every degree of freedom (i.e., a linear combination that reveals one unit of new information) even if it does not reveal an original packet immediately. Such ACKs enable a TCP-like sliding-window approach to network coding. Our scheme has the nice property that packet losses are essentially masked from the congestion control algorithm. Our algorithm therefore reacts to packet drops in a smooth manner, resulting in a novel and effective approach for congestion control over networks involving lossy links such as wireless links. Our experiments show that our algorithm achieves higher throughput compared to TCP in the presence of lossy wireless links. We also establish the soundness and fairness properties of our algorithm.

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arXiv2008

Network Coding for Speedup in Switches

We present a graph theoretic upper bound on speedup needed to achieve 100% throughput in a multicast switch using network coding. By bounding speedup, we show the equivalence between network coding and speedup in multicast switches - i.e. network coding, which is usually implemented using software, can in many cases substitute speedup, which is often achieved by adding extra switch fabrics. This bound is based on an approach to network coding problems called the "enhanced conflict graph". We show that the "imperfection ratio" of the enhanced conflict graph gives an upper bound on speedup. In particular, we apply this result to K-by-N switches with traffic patterns consisting of unicasts and broadcasts only to obtain an upper bound of min{(2K-1)/K, 2N/(N+1)}.

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arXiv2007

A Doubly Distributed Genetic Algorithm for Network Coding

We present a genetic algorithm which is distributed in two novel ways: along genotype and temporal axes. Our algorithm first distributes, for every member of the population, a subset of the genotype to each network node, rather than a subset of the population to each. This genotype distribution is shown to offer a significant gain in running time. Then, for efficient use of the computational resources in the network, our algorithm divides the candidate solutions into pipelined sets and thus the distribution is in the temporal domain, rather that in the spatial domain. This temporal distribution may lead to temporal inconsistency in selection and replacement, however our experiments yield better efficiency in terms of the time to convergence without incurring significant penalties.

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arXiv2007

Genetic Representations for Evolutionary Minimization of Network Coding Resources

We demonstrate how a genetic algorithm solves the problem of minimizing the resources used for network coding, subject to a throughput constraint, in a multicast scenario. A genetic algorithm avoids the computational complexity that makes the problem NP-hard and, for our experiments, greatly improves on sub-optimal solutions of established methods. We compare two different genotype encodings, which tradeoff search space size with fitness landscape, as well as the associated genetic operators. Our finding favors a smaller encoding despite its fewer intermediate solutions and demonstrates the impact of the modularity enforced by genetic operators on the performance of the algorithm.

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arXiv2007

Evolutionary Approaches to Minimizing Network Coding Resources

We wish to minimize the resources used for network coding while achieving the desired throughput in a multicast scenario. We employ evolutionary approaches, based on a genetic algorithm, that avoid the computational complexity that makes the problem NP-hard. Our experiments show great improvements over the sub-optimal solutions of prior methods. Our new algorithms improve over our previously proposed algorithm in three ways. First, whereas the previous algorithm can be applied only to acyclic networks, our new method works also with networks with cycles. Second, we enrich the set of components used in the genetic algorithm, which improves the performance. Third, we develop a novel distributed framework. Combining distributed random network coding with our distributed optimization yields a network coding protocol where the resources used for coding are optimized in the setup phase by running our evolutionary algorithm at each node of the network. We demonstrate the effectiveness of our approach by carrying out simulations on a number of different sets of network topologies.

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arXiv2007

On Coding for Reliable Communication over Packet Networks

We present a capacity-achieving coding scheme for unicast or multicast over lossy packet networks. In the scheme, intermediate nodes perform additional coding yet do not decode nor even wait for a block of packets before sending out coded packets. Rather, whenever they have a transmission opportunity, they send out coded packets formed from random linear combinations of previously received packets. All coding and decoding operations have polynomial complexity. We show that the scheme is capacity-achieving as long as packets received on a link arrive according to a process that has an average rate. Thus, packet losses on a link may exhibit correlation in time or with losses on other links. In the special case of Poisson traffic with i.i.d. losses, we give error exponents that quantify the rate of decay of the probability of error with coding delay. Our analysis of the scheme shows that it is not only capacity-achieving, but that the propagation of packets carrying "innovative" information follows the propagation of jobs through a queueing network, and therefore fluid flow models yield good approximations. We consider networks with both lossy point-to-point and broadcast links, allowing us to model both wireline and wireless packet networks.

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arXiv2006

Network Coding in a Multicast Switch

We consider the problem of serving multicast flows in a crossbar switch. We show that linear network coding across packets of a flow can sustain traffic patterns that cannot be served if network coding were not allowed. Thus, network coding leads to a larger rate region in a multicast crossbar switch. We demonstrate a traffic pattern which requires a switch speedup if coding is not allowed, whereas, with coding the speedup requirement is eliminated completely. In addition to throughput benefits, coding simplifies the characterization of the rate region. We give a graph-theoretic characterization of the rate region with fanout splitting and intra-flow coding, in terms of the stable set polytope of the 'enhanced conflict graph' of the traffic pattern. Such a formulation is not known in the case of fanout splitting without coding. We show that computing the offline schedule (i.e. using prior knowledge of the flow arrival rates) can be reduced to certain graph coloring problems. Finally, we propose online algorithms (i.e. using only the current queue occupancy information) for multicast scheduling based on our graph-theoretic formulation. In particular, we show that a maximum weighted stable set algorithm stabilizes the queues for all rates within the rate region.

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arXiv2006

A SIMO Fiber Aided Wireless Network Architecture

The concept of a fiber aided wireless network architecture (FAWNA) is introduced in [Ray et al., Allerton Conference 2005], which allows high-speed mobile connectivity by leveraging the speed of optical networks. In this paper, we consider a single-input, multiple-output (SIMO) FAWNA, which consists of a SIMO wireless channel and an optical fiber channel, connected through wireless-optical interfaces. We propose a scheme where the received wireless signal at each interface is quantized and sent over the fiber. Though our architecture is similar to that of the classical CEO problem, our problem is different from it. We show that the capacity of our scheme approaches the capacity of the architecture, exponentially with fiber capacity. We also show that for a given fiber capacity, there is an optimal operating wireless bandwidth and an optimal number of wireless-optical interfaces. The wireless-optical interfaces of our scheme have low complexity and do not require knowledge of the transmitter code book. They are also extendable to FAWNAs with large number of transmitters and interfaces and, offer adaptability to variable rates, changing channel conditions and node positions.

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arXiv2006

On Separation, Randomness and Linearity for Network Codes over Finite Fields

We examine the issue of separation and code design for networks that operate over finite fields. We demonstrate that source-channel (or source-network) separation holds for several canonical network examples like the noisy multiple access channel and the erasure degraded broadcast channel, when the whole network operates over a common finite field. This robustness of separation is predicated on the fact that noise and inputs are independent, and we examine the failure of separation when noise is dependent on inputs in multiple access channels. Our approach is based on the sufficiency of linear codes. Using a simple and unifying framework, we not only re-establish with economy the optimality of linear codes for single-transmitter, single-receiver channels and for Slepian-Wolf source coding, but also establish the optimality of linear codes for multiple access and for erasure degraded broadcast channels. The linearity allows us to obtain simple optimal code constructions and to study capacity regions of the noisy multiple access and the degraded broadcast channel. The linearity of both source and network coding blurs the delineation between source and network codes. While our results point to the fact that separation of source coding and channel coding is optimal in some canonical networks, we show that decomposing networks into canonical subnetworks may not be effective. Thus, we argue that it may be the lack of decomposability of a network into canonical network modules, rather than the lack of separation between source and channel coding, that presents major challenges for coding over networks.

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arXiv2006

On Non-coherent MIMO Channels in the Wideband Regime: Capacity and Reliability

We consider a multiple-input, multiple-output (MIMO) wideband Rayleigh block fading channel where the channel state is unknown to both the transmitter and the receiver and there is only an average power constraint on the input. We compute the capacity and analyze its dependence on coherence length, number of antennas and receive signal-to-noise ratio (SNR) per degree of freedom. We establish conditions on the coherence length and number of antennas for the non-coherent channel to have a "near coherent" performance in the wideband regime. We also propose a signaling scheme that is near-capacity achieving in this regime. We compute the error probability for this wideband non-coherent MIMO channel and study its dependence on SNR, number of transmit and receive antennas and coherence length. We show that error probability decays inversely with coherence length and exponentially with the product of the number of transmit and receive antennas. Moreover, channel outage dominates error probability in the wideband regime. We also show that the critical as well as cut-off rates are much smaller than channel capacity in this regime.

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arXiv2006

Minimum-Cost Multicast over Coded Packet Networks

We consider the problem of establishing minimum-cost multicast connections over coded packet networks, i.e. packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomial-time solvable optimization problem, and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimum-cost multicast. By contrast, establishing minimum-cost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved.

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arXiv2005

Further Results on Coding for Reliable Communication over Packet Networks

In "On Coding for Reliable Communication over Packet Networks" (Lun, Medard, and Effros, Proc. 42nd Annu. Allerton Conf. Communication, Control, and Computing, 2004), a capacity-achieving coding scheme for unicast or multicast over lossy wireline or wireless packet networks is presented. We extend that paper's results in two ways: First, we extend the network model to allow packets received on a link to arrive according to any process with an average rate, as opposed to the assumption of Poisson traffic with i.i.d. losses that was previously made. Second, in the case of Poisson traffic with i.i.d. losses, we derive error exponents that quantify the rate at which the probability of error decays with coding delay.

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