Cache-Aided Coded Multicast for Correlated Sources

The combination of edge caching and coded multicasting is a promising approach to improve the efficiency of content delivery over cache-aided networks. The global caching gain resulting from content overlap distributed across the network in current solutions is limited due to the increasingly personalized nature of the content consumed by users. In this paper, the cache-aided coded multicast problem is generalized to account for the correlation among the network content by formulating a source compression problem with distributed side information. A correlation-aware achievable scheme is proposed and an upper bound on its performance is derived. It is shown that considerable load reductions can be achieved, compared to state of the art correlation-unaware schemes, when caching and delivery phases specifically account for the correlation among the content files.Comment: In proceeding of IEEE International Symposium on Turbo Codes and Iterative Information Processing (ISTC), 201

Correlation-Aware Distributed Caching and Coded Delivery

Cache-aided coded multicast leverages side information at wireless edge caches to efficiently serve multiple groupcast demands via common multicast transmissions, leading to load reductions that are proportional to the aggregate cache size. However, the increasingly unpredictable and personalized nature of the content that users consume challenges the efficiency of existing caching-based solutions in which only exact content reuse is explored. This paper generalizes the cache-aided coded multicast problem to a source compression with distributed side information problem that specifically accounts for the correlation among the content files. It is shown how joint file compression during the caching and delivery phases can provide load reductions that go beyond those achieved with existing schemes. This is accomplished through a lower bound on the fundamental rate-memory trade-off as well as a correlation-aware achievable scheme, shown to significantly outperform state-of-the-art correlation-unaware solutions, while approaching the limiting rate-memory trade-off.Comment: In proceeding of IEEE Information Theory Workshop (ITW), 201

Support Recovery with Sparsely Sampled Free Random Matrices

Consider a Bernoulli-Gaussian complex $n$-vector whose components are $V_i = X_i B_i$, with X_i \sim \Cc\Nc(0,\Pc_x) and binary $B_i$ mutually independent and iid across $i$. This random $q$-sparse vector is multiplied by a square random matrix \Um, and a randomly chosen subset, of average size $n p$, $p \in [0,1]$, of the resulting vector components is then observed in additive Gaussian noise. We extend the scope of conventional noisy compressive sampling models where \Um is typically %A16 the identity or a matrix with iid components, to allow \Um satisfying a certain freeness condition. This class of matrices encompasses Haar matrices and other unitarily invariant matrices. We use the replica method and the decoupling principle of Guo and Verd\'u, as well as a number of information theoretic bounds, to study the input-output mutual information and the support recovery error rate in the limit of $n \to \infty$. We also extend the scope of the large deviation approach of Rangan, Fletcher and Goyal and characterize the performance of a class of estimators encompassing thresholded linear MMSE and $\ell_1$ relaxation

Broadcast Caching Networks with Two Receivers and Multiple Correlated Sources

The correlation among the content distributed across a cache-aided broadcast network can be exploited to reduce the delivery load on the shared wireless link. This paper considers a two-user three-file network with correlated content, and studies its fundamental limits for the worst-case demand. A class of achievable schemes based on a two-step source coding approach is proposed. Library files are first compressed using Gray-Wyner source coding, and then cached and delivered using a combination of correlation-unaware cache-aided coded multicast schemes. The second step is interesting in its own right and considers a multiple-request caching problem, whose solution requires coding in the placement phase. A lower bound on the optimal peak rate-memory trade-off is derived, which is used to evaluate the performance of the proposed scheme. It is shown that for symmetric sources the two-step strategy achieves the lower bound for large cache capacities, and it is within half of the joint entropy of two of the sources conditioned on the third source for all other cache sizes.Comment: in Proceedings of Asilomar Conference on Signals, Systems and Computers, Pacific Grove, California, November 201

Caching and Coded Multicasting: Multiple Groupcast Index Coding

The capacity of caching networks has received considerable attention in the past few years. A particularly studied setting is the case of a single server (e.g., a base station) and multiple users, each of which caches segments of files in a finite library. Each user requests one (whole) file in the library and the server sends a common coded multicast message to satisfy all users at once. The problem consists of finding the smallest possible codeword length to satisfy such requests. In this paper we consider the generalization to the case where each user places $L \geq 1$ requests. The obvious naive scheme consists of applying $L$ times the order-optimal scheme for a single request, obtaining a linear in $L$ scaling of the multicast codeword length. We propose a new achievable scheme based on multiple groupcast index coding that achieves a significant gain over the naive scheme. Furthermore, through an information theoretic converse we find that the proposed scheme is approximately optimal within a constant factor of (at most) $18$.Comment: 5 pages, 1 figure, to appear in GlobalSIP14, Dec. 201

Hypergraph-Based Analysis of Clustered Cooperative Beamforming with Application to Edge Caching

The evaluation of the performance of clustered cooperative beamforming in cellular networks generally requires the solution of complex non-convex optimization problems. In this letter, a framework based on a hypergraph formalism is proposed that enables the derivation of a performance characterization of clustered cooperative beamforming in terms of per-user degrees of freedom (DoF) via the efficient solution of a coloring problem. An emerging scenario in which clusters of cooperative base stations (BSs) arise is given by cellular networks with edge caching. In fact, clusters of BSs that share the same requested files can jointly beamform the corresponding encoded signals. Based on this observation, the proposed framework is applied to obtain quantitative insights into the optimal use of cache and backhaul resources in cellular systems with edge caching. Numerical examples are provided to illustrate the merits of the proposed framework.Comment: 10 pages, 5 figures, Submitte