Mohammad Ali Maddah-Ali

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 with previously known schemes. In particular, the improvement can be on the order of the number of users in the network. In addition, 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.

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 multiple-input multiple-output (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 an MIMO broadcast channel with transmit antennas and receivers each with 1 receive antenna, K/1+1/2+···+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.

Real Interference Alignment: Exploiting the Potential of Single Antenna Systems

In this paper, we develop the machinery of real interference alignment. This machinery is extremely powerful in achieving the sum degrees of freedom (DoF) of single antenna systems. The scheme of real interference alignment is based on designing single-layer and multilayer constellations used for modulating information messages at the transmitters. We show that constellations can be aligned in a similar fashion as that of vectors in multiple antenna systems and space can be broken up into fractional dimensions. The performance analysis of the signaling scheme makes use of a recent result in the field of Diophantine approximation, which states that the convergence part of the Khintchine-Groshev theorem holds for points on nondegenerate manifolds. Using real interference alignment, we obtain the sum DoF of two model channels, namely the Gaussian interference channel (IC) and the X channel. It is proved that the sum DoF of the K-user IC is (K/2) for almost all channel parameters. We also prove that the sum DoF of the X-channel with K transmitters and M receivers is (K M/K + M - 1) for almost all channel parameters.

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 multicasting opportunities, even for users with different demands, through coding across data streams. These simultaneous 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 simultaneous coded-multicasting opportunities, and hence achieves a rate close to the centralized scheme.

Signaling over MIMO Multi-Base Systems: Combination of Multi-Access and Broadcast Schemes

A new structure for multi-base systems is studied in which each user receives data from two nearby base stations, rather than only from the strongest one. This system can be considered as a combination of broadcast and multi-access channels. By taking advantages of both perspectives, an achievable rate region for a discrete memoryless channel modeled by Pr(y1,y2|x1,x2 ) is derived. In this model, x1 and x2 represent the transmitted signals by the transmitter one and two, respectively, and y1 and y2 denote the received signals by the receiver one and two, respectively. In this derivation, it is assumed that each transmitter is unaware of the data of the other transmitter, and therefore x1 and x2 are independent. To investigate the advantage of this scheme, an efficient signaling method which works at a corner point of the achievable region for multiple-antenna scenarios is developed. In the proposed scheme, each base station only requires the state information of the channels between the other base station and each user. In this paper, the signaling scheme is elaborated for the case that each transmitter/receiver is equipped with three antennas. It is proven that in such a scenario, the multiplexing gain of four is achievable, which outperforms any other conventional schemes

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 showed that in a MIMO broadcast channel with K transmit antennas and K receivers each with 1 receive antenna, equation (> 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 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.

Coded caching with nonuniform demands

We consider a network consisting of a file server connected through a shared link to a number of users, each equipped with a cache. Knowing the popularity distribution of the files, the goal is to optimally populate the caches, such as to minimize the expected load of the shared link. For a single cache, it is well known that storing the most popular files is optimal in this setting. However, we show here that this is no longer the case for multiple caches. Indeed, caching only the most popular files can be highly suboptimal. Instead, a fundamentally different approach is needed, in which the cache contents are used as side information for coded communication over the shared link. We propose such a coded caching scheme and prove that it is close to optimal.

Fundamental limits of caching

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

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 locally deliver the part of the content, 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 paper, 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 the layers can simultaneously operate at approximately the minimum rate.

Cache-aided interference channels

Over the past decade, the bulk of wireless traffic has shifted from speech to content. This shift creates the opportunity to cache part of the content in memories closer to the end users, for example in base stations. Most of the prior literature focuses on the reduction of load in the backhaul and core networks due to caching, i.e., on the benefits caching offers for the wireline communication link between the origin server and the caches. In this paper, we are instead interested in the benefits caching can offer for the wireless communication link between the caches and the end users. To quantify the gains of caching for this wireless link, we consider an interference channel in which each transmitter is equipped with an isolated cache memory. Communication takes place in two phases, a content placement phase followed by a content delivery phase. The objective is to design both the placement and the delivery phases to maximize the rate in the delivery phase in response to any possible user demands. Focusing on the three-user case, we show that through careful joint design of these phases, we can reap three distinct benefits from caching: a load balancing gain, an interference cancellation gain, and an interference alignment gain. In our proposed scheme, load balancing is achieved through a specific file splitting and placement, creating a particular pattern of content overlap at the caches. This overlap allows to implement interference cancellation. Further, it allows us to construct several virtual transmitters, each responsible for a part of the requested content, which increases interference alignment possibilities.