Content Caching and Delivery over Heterogeneous Wireless Networks

Emerging heterogeneous wireless architectures consist of a dense deployment of local-coverage wireless access points (APs) with high data rates, along with sparsely-distributed, large-coverage macro-cell base stations (BS). We design a coded caching-and-delivery scheme for such architectures that equips APs with storage, enabling content pre-fetching prior to knowing user demands. Users requesting content are served by connecting to local APs with cached content, as well as by listening to a BS broadcast transmission. For any given content popularity profile, the goal is to design the caching-and-delivery scheme so as to optimally trade off the transmission cost at the BS against the storage cost at the APs and the user cost of connecting to multiple APs. We design a coded caching scheme for non-uniform content popularity that dynamically allocates user access to APs based on requested content. We demonstrate the approximate optimality of our scheme with respect to information-theoretic bounds. We numerically evaluate it on a YouTube dataset and quantify the trade-off between transmission rate, storage, and access cost. Our numerical results also suggest the intriguing possibility that, to gain most of the benefits of coded caching, it suffices to divide the content into a small number of popularity classes.Comment: A shorter version is to appear in IEEE INFOCOM 201

Effect of Number of Users in Multi-level Coded Caching

It has been recently established that joint design of content delivery and storage (coded caching) can significantly improve performance over conventional caching. This has also been extended to the case when content has non-uniform popularity through several models. In this paper we focus on a multi-level popularity model, where content is divided into levels based on popularity. We consider two extreme cases of user distribution across caches for the multi-level popularity model: a single user per cache (single-user setup) versus a large number of users per cache (multi-user setup). When the capacity approximation is universal (independent of number of popularity levels as well as number of users, files and caches), we demonstrate a dichotomy in the order-optimal strategies for these two extreme cases. In the multi-user case, sharing memory among the levels is order-optimal, whereas for the single-user case clustering popularity levels and allocating all the memory to them is the order-optimal scheme. In proving these results, we develop new information-theoretic lower bounds for the problem.Comment: 13 pages; 2 figures. A shorter version is to appear in IEEE ISIT 201

Caching with Partial Adaptive Matching

We study the caching problem when we are allowed to match each user to one of a subset of caches after its request is revealed. We focus on non-uniformly popular content, specifically when the file popularities obey a Zipf distribution. We study two extremal schemes, one focusing on coded server transmissions while ignoring matching capabilities, and the other focusing on adaptive matching while ignoring potential coding opportunities. We derive the rates achieved by these schemes and characterize the regimes in which one outperforms the other. We also compare them to information-theoretic outer bounds, and finally propose a hybrid scheme that generalizes ideas from the two schemes and performs at least as well as either of them in most memory regimes.Comment: 35 pages, 7 figures. Shorter versions have appeared in IEEE ISIT 2017 and IEEE ITW 201

Coding with Encoding Uncertainty

We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding uncertainty as erasures on the edges in the factor graph of the encoder generator matrix. We first take a worst-case approach and find the maximum tolerable number of erasures for perfect error correction. Next, we take a probabilistic approach and derive a sufficient condition on the rate of a set of codes, such that decoding error probability vanishes as blocklength tends to infinity. In both scenarios, due to the inherent asymmetry of the problem, we derive the results from first principles, which indicates that robustness to encoding errors requires new properties of codes different from classical properties.Comment: 12 pages; a shorter version of this work will appear in the proceedings of ISIT 201

Coded Content Caching for Wireless Networks

The increase in mobile Internet usage has created a need to optimize content delivery in cellular networks.In emerging technologies such as 5G, heterogeneous networks are proposed, which consist of sparsely deployed cellular base stations (BS) with wide coverage but low data rate, combined with a dense network of wireless access points (AP) of small coverage but relatively high data rate.We envisage equipping the APs with a local cache.When a group of users request some files, their demands are served by a (common) broadcast from one or more BSs, which is aided by side information placed a priori in the APs.Therefore, there is a tradeoff between the size of the cache and the size of the broadcast.Our goal is to design schemes that optimize this tradeoff.Traditional caching techniques, which have proved efficient in the wired Internet, are insufficient to handle the explosion in multimedia demand in wireless networks.The seminal work by Maddah-Ali and Niesen [``Fundamental limits of caching,'' IEEE Transactions on Information Theory, May 2014] introduced an information-theoretic framework to study this problem and proposed the so-called ``coded caching'' technique that takes advantage of the broadcast nature of wireless to send coded multicast messages to many users at once, thus greatly improving the transmission rate.This original work assumed a caching system with an error-free broadcast link between the content library and the users, focused on equally popular files, and assumed that each user has one exclusive local cache.Inspired by this work, this thesis studies more general coded caching problems within this information-theoretic framework.Broadly speaking, we focus on non-uniform content popularity as well as more general network topologies.First, we consider a system where the files desired by the users are not all equally popular.We adopt a ``multi-level'' popularity model where files are partitioned into multiple popularity classes.Under this model, we study the behavior of the system as the total number of users, as compared to the number of caches, varies.Furthermore, we allow a more complex topology by requiring some users to connect to multiple caches at once.We find approximately optimal strategies for the two extreme cases: when the number of users per cache is very large, and when each cache has exactly one user.An interesting dichotomy is observed where the approximately optimal strategies required for these two extremes are very different.Finally, we provide a heuristic for ``discretizing'' common popularity distributions such as Zipf into multiple levels, and numerically evaluate its performance.Second, we study the caching problem when we are allowed to assign users to caches after their demands are known, under some restrictions.Specifically, we divide the caches into several clusters, and we assume that each user can be assigned to one cache from a specific cluster and that each cache can serve no more than one user.Focusing on a stochastic Zipf popularity model, we find that there are regimes in which coded caching is no longer efficient.Instead, a strategy that consists in replicating files across clusters and performs an uncoded delivery dominates certain regimes.We compare these two schemes and find the regimes in which each is more efficient, as a function of cache memory, cluster size, and skewness of popularity.Finally, we show that each scheme is approximately optimal in some of these regimes.Third, we return to the uniform popularity model in order to study more complicated networks than the error-free broadcast network.Our main focus is on Gaussian interference networks, where caches are placed at both the transmitters (BSs) and the receivers (APs).We propose a separation-based approach that creates separate network and physical layers, with a multiple-multicast message set to act as an interface between them.At the physical layer, we focus on transmitting this message set across the interference channel; at the network layer, we solve the caching problem using the message set as a set of error-free links replacing the channel.We show that this architecture is approximately optimal under high SNR.Among the implications of this result is that placing common information between the transmitters cannot give more than a constant-factor benefit.Moreover, we show that, when the receiver memory is large, a small number of transmitters is enough to obtain most of the benefits

Coded Caching for Multi-level Popularity and Access

To address the exponentially rising demand for wireless content, the use of caching is emerging as a potential solution. It has been recently established that joint design of content delivery and storage (coded caching) can significantly improve performance over conventional caching. Coded caching is well suited to emerging heterogeneous wireless architectures which consist of a dense deployment of local-coverage wireless access points (APs) with high data rates, along with sparsely-distributed, large-coverage macro-cell base stations (BS). This enables design of coded caching-and-delivery schemes that equip APs with storage, and place content in them in a way that creates coded-multicast opportunities for combining with macrocell broadcast to satisfy users even with different demands. Such coded-caching schemes have been shown to be order-optimal with respect to the BS transmission rate, for a system with single-level content, i.e., one where all content is uniformly popular. In this paper, we consider a system with non-uniform popularity content which is divided into multiple levels, based on varying degrees of popularity. The main contribution of this paper is the derivation of an order-optimal scheme which judiciously shares cache memory among files with different popularities. To show order-optimality we derive new information-theoretic lower bounds, which use a sliding-window entropy inequality, effectively creating a non-cut-set bound. We also extend the ideas to when users can access multiple caches along with the broadcast. Finally, we consider two extreme cases of user distribution across caches for the multi-level popularity model: a single user per cache (single-user setup) versus a large number of users per cache (multi-user setup), and demonstrate a dichotomy in the order-optimal strategies for these two extreme cases