arXiv subjects

Mohammad Ali Maddah-Ali

Publications and source records attributed to Mohammad Ali Maddah-Ali.

90 records · Page 5Linked to original sources

arXiv2015

Coded MapReduce

MapReduce is a commonly used framework for executing data-intensive jobs on distributed server clusters. We introduce a variant implementation of MapReduce, namely "Coded MapReduce", to substantially reduce the inter-server communication load for the shuffling phase of MapReduce, and thus accelerating its execution. The proposed Coded MapReduce exploits the repetitive mapping of data blocks at different servers to create coding opportunities in the shuffling phase to exchange (key,value) pairs among servers much more efficiently. We demonstrate that Coded MapReduce can cut down the total inter-server communication load by a multiplicative factor that grows linearly with the number of servers in the system and it achieves the minimum communication load within a constant multiplicative factor. We also analyze the tradeoff between the "computation load" and the "communication load" of Coded MapReduce.

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arXiv2015

Cooperation Alignment for Distributed Interference Management

We consider a cooperative Gaussian interference channel in which each receiver must decode its intended message locally, with the help of cooperation either at the receivers side or at the transmitter side. In the case of receiver cooperation, the receivers can process and share information through limited capacity backhaul links. In contrast to various previously considered distributed antenna architectures, where processing is utterly performed in a centralized fashion, the model considered in this paper aims to capture the essence of decentralized processing, allowing for a more general class of "interactive" interference management strategies. Focusing on the three-user case, we characterize the fundamental tradeoff between the achievable communication rates and the corresponding backhaul cooperation rate, in terms of degrees of freedom (DoF). Surprisingly, we show that the optimum communication-cooperation tradeoff per user remains the same when we move from two-user to three-user interference channels. In the absence of cooperation, this is due to interference alignment, which keeps the fraction of communication dimensions wasted for interference unchanged. When backhaul cooperation is available, we develop a new idea that we call cooperation alignment, which guarantees that the average (per user) backhaul load remains the same as we increase the number of users. In the case of transmitter cooperation, the transmitters can form their jointly precoded signals through an interactive protocol over the backhaul. In this case, we show that the optimal (per user) tradeoff between the achievable communication rates and the corresponding backhaul cooperation rate in the three-user case is the same as for receiver cooperation.

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arXiv2015

Blind Index Coding

We introduce the blind index coding (BIC) problem, in which a single sender communicates distinct messages to multiple users over a shared channel. Each user has partial knowledge of each message as side information. However, unlike classic index coding, in BIC, the sender is uncertain of what side information is available to each user. In particular, the sender only knows the amount of bits in each user's side information but not its content. This problem can arise naturally in caching and wireless networks. In order to blindly exploit side information in the BIC problem, we develop a hybrid coding scheme that XORs uncoded bits of a subset of messages with random combinations of bits from other messages. This scheme allows us to strike the right balance between maximizing the transmission rate to each user and minimizing the interference leakage to others. We also develop a general outer bound, which relies on a strong data processing inequality to effectively capture the senders uncertainty about the users' side information. Additionally, we consider the case where communication takes place over a shared wireless medium, modeled by an erasure broadcast channel, and show that surprisingly, combining repetition coding with hybrid coding improves the achievable rate region and outperforms alternative strategies of coping with channel erasure and while blindly exploiting side information.

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arXiv2014

Cellular Interference Alignment: Omni-Directional Antennas and Asymmetric Configurations

Although interference alignment (IA) can theoretically achieve the optimal degrees of freedom (DoFs) in the $K$-user Gaussian interference channel, its direct application comes at the prohibitive cost of precoding over exponentially-many signaling dimensions. On the other hand, it is known that practical "one-shot" IA precoding (i.e., linear schemes without symbol expansion) provides a vanishing DoFs gain in large fully-connected networks with generic channel coefficients. In our previous work, we introduced the concept of "Cellular IA" for a network topology induced by hexagonal cells with sectors and nearest-neighbor interference. Assuming that neighboring sectors can exchange decoded messages (and not received signal samples) in the uplink, we showed that linear one-shot IA precoding over $M$ transmit/receive antennas can achieve the optimal $M/2$ DoFs per user. In this paper we extend this framework to networks with omni-directional (non-sectorized) cells and consider the practical scenario where users have $2$ antennas, and base-stations have $2$, $3$ or $4$ antennas. In particular, we provide linear one-shot IA schemes for the $2\times 2$, $2\times3$ and $2\times 4$ cases, and show the achievability of $3/4$, $1$ and $7/6$ DoFs per user, respectively. DoFs converses for one-shot schemes require the solution of a discrete optimization problem over a number of variables that grows with the network size. We develop a new approach to transform such challenging optimization problem into a tractable linear program (LP) with significantly fewer variables. This approach is used to show that the achievable $3/4$ DoFs per user are indeed optimal for a large (extended) cellular network with $2\times 2$ links.

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arXiv2014

Capacity Results for Binary Fading Interference Channels with Delayed CSIT

To study the effect of lack of up-to-date channel state information at the transmitters (CSIT), we consider two-user binary fading interference channels with Delayed-CSIT. We characterize the capacity region for such channels under homogeneous assumption where channel gains have identical and independent distributions across time and space, eliminating the possibility of exploiting time/space correlation. We introduce and discuss several novel coding opportunities created by outdated CSIT that can enlarge the achievable rate region. The capacity-achieving scheme relies on accurate combination, concatenation, and merging of these opportunities, depending on the channel statistics. The outer-bounds are based on an extremal inequality we develop for a binary broadcast channel with Delayed-CSIT. We further extend the results and characterize the capacity region when output feedback links are available from the receivers to the transmitters in addition to the delayed knowledge of the channel state information. We also discuss the extension of our results to the non-homogeneous setting.

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arXiv2014

Coded Caching for Delay-Sensitive Content

Coded caching is a recently proposed technique that achieves significant performance gains for cache networks compared to uncoded caching schemes. However, this substantial coding gain is attained at the cost of large delivery delay, which is not tolerable in delay-sensitive applications such as video streaming. In this paper, we identify and investigate the tradeoff between the performance gain of coded caching and the delivery delay. We propose a computationally efficient caching algorithm that provides the gains of coding and respects delay constraints. The proposed algorithm achieves the optimum performance for large delay, but still offers major gains for small delay. These gains are demonstrated in a practical setting with a video-streaming prototype.

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arXiv2014

On Uplink-Downlink Duality for Cellular IA

In our previous work we considered the uplink of a hexagonal cellular network topology and showed that linear "one-shot" interference alignment (IA) schemes are able to achieve the optimal degrees of freedom (DoFs) per user, under a decoded-message passing framework that allows base-stations to exchange their own decoded messages over local backhaul links. In this work, we provide the dual framework for the downlink of cellular networks with the same backhaul architecture, and show that for every "one-shot" IA scheme that can achieve $d$ DoFs per user in the uplink, there exists a dual "one-shot" IA scheme that can achieve the same DoFs in the downlink. To enable "Cellular IA" for the downlink, base-stations will now use the same local backhaul links to exchange quantized versions of the dirty-paper precoded signals instead of user messages.

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arXiv2014

Hierarchical Coded Caching

Caching of popular content during off-peak hours is a strategy to reduce network loads during peak hours. Recent work has shown significant benefits of designing such caching strategies not only to deliver part of the content locally, but also to provide coded multicasting opportunities even among users with different demands. Exploiting both of these gains was shown to be approximately optimal for caching systems with a single layer of caches. Motivated by practical scenarios, we consider in this work a hierarchical content delivery network with two layers of caches. We propose a new caching scheme that combines two basic approaches. The first approach provides coded multicasting opportunities within each layer; the second approach provides coded multicasting opportunities across multiple layers. By striking the right balance between these two approaches, we show that the proposed scheme achieves the optimal communication rates to within a constant multiplicative and additive gap. We further show that there is no tension between the rates in each of the two layers up to the aforementioned gap. Thus, both layers can simultaneously operate at approximately the minimum rate.

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arXiv2014

Decentralized Coded Caching Attains Order-Optimal Memory-Rate Tradeoff

Replicating or caching popular content in memories distributed across the network is a technique to reduce peak network loads. Conventionally, the main performance gain of this caching was thought to result from making part of the requested data available closer to end users. Instead, we recently showed that a much more significant gain can be achieved by using caches to create coded-multicasting opportunities, even for users with different demands, through coding across data streams. These coded-multicasting opportunities are enabled by careful content overlap at the various caches in the network, created by a central coordinating server. In many scenarios, such a central coordinating server may not be available, raising the question if this multicasting gain can still be achieved in a more decentralized setting. In this paper, we propose an efficient caching scheme, in which the content placement is performed in a decentralized manner. In other words, no coordination is required for the content placement. Despite this lack of coordination, the proposed scheme is nevertheless able to create coded-multicasting opportunities and achieves a rate close to the optimal centralized scheme.

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arXiv2014

Cellular Interference Alignment

Interference alignment promises that, in Gaussian interference channels, each link can support half of a degree of freedom (DoF) per pair of transmit-receive antennas. However, in general, this result requires to precode the data bearing signals over a signal space of asymptotically large diversity, e.g., over an infinite number of dimensions for time-frequency varying fading channels, or over an infinite number of rationally independent signal levels, in the case of time-frequency invariant channels. In this work we consider a wireless cellular system scenario where the promised optimal DoFs are achieved with linear precoding in one-shot (i.e., over a single time-frequency slot). We focus on the uplink of a symmetric cellular system, where each cell is split into three sectors with orthogonal intra-sector multiple access. In our model, interference is "local", i.e., it is due to transmitters in neighboring cells only. We consider a message-passing backhaul network architecture, in which nearby sectors can exchange already decoded messages and propose an alignment solution that can achieve the optimal DoFs. To avoid signaling schemes relying on the strength of interference, we further introduce the notion of \emph{topologically robust} schemes, which are able to guarantee a minimum rate (or DoFs) irrespectively of the strength of the interfering links. Towards this end, we design an alignment scheme which is topologically robust and still achieves the same optimum DoFs.

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arXiv2014

Fundamental Limits of Caching

Caching is a technique to reduce peak traffic rates by prefetching popular content into memories at the end users. Conventionally, these memories are used to deliver requested content in part from a locally cached copy rather than through the network. The gain offered by this approach, which we term local caching gain, depends on the local cache size (i.e, the memory available at each individual user). In this paper, we introduce and exploit a second, global, caching gain not utilized by conventional caching schemes. This gain depends on the aggregate global cache size (i.e., the cumulative memory available at all users), even though there is no cooperation among the users. To evaluate and isolate these two gains, we introduce an information-theoretic formulation of the caching problem focusing on its basic structure. For this setting, we propose a novel coded caching scheme that exploits both local and global caching gains, leading to a multiplicative improvement in the peak rate compared to previously known schemes. In particular, the improvement can be on the order of the number of users in the network. Moreover, we argue that the performance of the proposed scheme is within a constant factor of the information-theoretic optimum for all values of the problem parameters.

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arXiv2013

Communication Through Collisions: Opportunistic Utilization of Past Receptions

When several wireless users are sharing the spectrum, packet collision is a simple, yet widely used model for interference. Under this model, when transmitters cause interference at any of the receivers, their collided packets are discarded and need to be retransmitted. However, in reality, that receiver can still store its analog received signal and utilize it for decoding the packets in the future (for example, by successive interference cancellation techniques). In this work, we propose a physical layer model for wireless packet networks that allows for such flexibility at the receivers. We assume that the transmitters will be aware of the state of the channel (i.e. when and where collisions occur, or an unintended receiver overhears the signal) with some delay, and propose several coding opportunities that can be utilized by the transmitters to exploit the available signal at the receivers for interference management (as opposed to discarding them). We analyze the achievable throughput of our strategy in a canonical interference channel with two transmitter-receiver pairs, and demonstrate the gain over conventional schemes. By deriving an outer-bound, we also prove the optimality of our scheme for the corresponding model.

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arXiv2013

Online Coded Caching

We consider a basic content distribution scenario consisting of a single origin server connected through a shared bottleneck link to a number of users each equipped with a cache of finite memory. The users issue a sequence of content requests from a set of popular files, and the goal is to operate the caches as well as the server such that these requests are satisfied with the minimum number of bits sent over the shared link. Assuming a basic Markov model for renewing the set of popular files, we characterize approximately the optimal long-term average rate of the shared link. We further prove that the optimal online scheme has approximately the same performance as the optimal offline scheme, in which the cache contents can be updated based on the entire set of popular files before each new request. To support these theoretical results, we propose an online coded caching scheme termed coded least-recently sent (LRS) and simulate it for a demand time series derived from the dataset made available by Netflix for the Netflix Prize. For this time series, we show that the proposed coded LRS algorithm significantly outperforms the popular least-recently used (LRU) caching algorithm.

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arXiv2012

Completely Stale Transmitter Channel State Information is Still Very Useful

Transmitter channel state information (CSIT) is crucial for the multiplexing gains offered by advanced interference management techniques such as multiuser MIMO and interference alignment. Such CSIT is usually obtained by feedback from the receivers, but the feedback is subject to delays. The usual approach is to use the fed back information to predict the current channel state and then apply a scheme designed assuming perfect CSIT. When the feedback delay is large compared to the channel coherence time, such a prediction approach completely fails to achieve any multiplexing gain. In this paper, we show that even in this case, the completely stale CSI is still very useful. More concretely, we show that in a MIMO broadcast channel with $K$ transmit antennas and $K$ receivers each with 1 receive antenna, $\frac{K}{1+1/2+ ...+ \frac{1}{K}} (> 1) $ degrees of freedom is achievable even when the fed back channel state is completely independent of the current channel state. Moreover, we establish that if all receivers have independent and identically distributed channels, then this is the optimal number of degrees of freedom achievable. In the optimal scheme, the transmitter uses the fed back CSI to learn the side information that the receivers receive from previous transmissions rather than to predict the current channel state. Our result can be viewed as the first example of feedback providing a degree-of-freedom gain in memoryless channels.

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arXiv2010

A Fixed Precoding Approach to Achieve the Degrees of Freedom in X channel

This paper aims to provide a fixed precoding scheme to achieve the Degrees of Freedom DoF of the generalized ergodic X channel. This is achieved through using the notion of ergodic interference alignment technique. Accordingly, in the proposed method the transmitters do not require to know the full channel state information, while this assumption is the integral part of existing methods. Instead, a finite-rate feed-back channel is adequate to achieve the DoF. In other words, it is demonstrated that quantized versions of channel gains are adequate to achieve theDOF. To get an insight regarding the functionality of the proposed method, first we rely on finite field channel models, and then extend the terminology to more realistic cases, including dispersive fading channels in the presence of quantizer. Accordingly, in a Rayliegh fading environment, it is shown a feedback rate of 2log(p)+Theta(log(log(p))) can provide the DoF, where $p$ is the total transmit power.

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arXiv2009

On the Degrees of Freedom of the Compound MIMO Broadcast Channels with Finite States

Multiple-antenna broadcast channels with $M$ transmit antennas and $K$ single-antenna receivers is considered, where the channel of receiver $r$ takes one of the $J_r$ finite values. It is assumed that the channel states of each receiver are randomly selected from $\mathds{R}^{M\times 1}$ (or from $\mathds{C}^{M\times 1}$). It is shown that no matter what $J_r$ is, the degrees of freedom (DoF) of $\frac{MK}{M+K-1}$ is achievable. The achievable scheme relies on the idea of interference alignment at receivers, without exploiting the possibility of cooperation among transmit antennas. It is proven that if $J_r \geq M$, $r=1,...,K$, this scheme achieves the optimal DoF. This results implies that when the uncertainty of the base station about the channel realization is considerable, the system loses the gain of cooperation. However, it still benefits from the gain of interference alignment. In fact, in this case, the compound broadcast channel is treated as a compound X channel. Moreover, it is shown that when the base station knows the channel states of some of the receivers, a combination of transmit cooperation and interference alignment would achieve the optimal DoF. Like time-invariant $K$-user interference channels, the naive vector-space approaches of interference management seem insufficient to achieve the optimal DoF of this channel. In this paper, we use the Number-Theory approach of alignment, recently developed by Motahari et al.[1]. We extend the approach of [1] to complex channels as well, therefore all the results that we present are valid for both real and complex channels.

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arXiv2007

On The Capacity Of Time-Varying Channels With Periodic Feedback

The capacity of time-varying channels with periodic feedback at the transmitter is evaluated. It is assumed that the channel state information is perfectly known at the receiver and is fed back to the transmitter at the regular time-intervals. The system capacity is investigated in two cases: i) finite state Markov channel, and ii) additive white Gaussian noise channel with time-correlated fading. In the first case, it is shown that the capacity is achievable by multiplexing multiple codebooks across the channel. In the second case, the channel capacity and the optimal adaptive coding is obtained. It is shown that the optimal adaptation can be achieved by a single Gaussian codebook, while adaptively allocating the total power based on the side information at the transmitter.

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arXiv2007

Optimal Order of Decoding for Max-Min Fairness in $K$-User Memoryless Interference Channels

A $K$-user memoryless interference channel is considered where each receiver sequentially decodes the data of a subset of transmitters before it decodes the data of the designated transmitter. Therefore, the data rate of each transmitter depends on (i) the subset of receivers which decode the data of that transmitter, (ii) the decoding order, employed at each of these receivers. In this paper, a greedy algorithm is developed to find the users which are decoded at each receiver and the corresponding decoding order such that the minimum rate of the users is maximized. It is proven that the proposed algorithm is optimal.

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