/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

This comprehensive treatment of network information theory and its applications provides the first unified coverage of both classical and recent results. With an approach that balances the introduction of new models and new coding techniques, readers are guided through Shannon's point-to-point information theory, single-hop networks, multihop networks, and extensions to distributed computing, secrecy, wireless communication, and networking. Elementary mathematical tools and techniques are used throughout, requiring only basic knowledge of probability, whilst unified proofs of coding theorems are based on a few simple lemmas, making the text accessible to newcomers. Key topics covered include successive cancellation and superposition coding, MIMO wireless communication, network coding, and cooperative relaying. Also covered are feedback and interactive communication, capacity approximations and scaling laws, and asynchronous and random access channels. This book is ideal for use in the classroom, for self-study, and as a reference for researchers and engineers in industry and academia.

Network Information Theory

Information Theory and Reliable Communication

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.

Fundamental Limits of Caching

Device-to-device (D2D) communications was initially proposed in cellular networks as a new paradigm for enhancing network performance. The emergence of new applications such as content distribution and location-aware advertisement introduced new user cases for D2D communications in cellular networks. The initial studies showed that D2D communications has advantages such as increased spectral efficiency and reduced communication delay. However, this communication mode introduces complications in terms of interference control overhead and protocols that are still open research problems. The feasibility of D2D communications in Long-Term Evolution Advanced is being studied by academia, industry, and standardization bodies. To date, there are more than 100 papers available on D2D communications in cellular networks, but there is no survey on this field. In this paper, we provide a taxonomy based on the D2D communicating spectrum and review the available literature extensively under the proposed taxonomy. Moreover, we provide new insights into the over-explored and under-explored areas that lead us to identify open research problems of D2D communications in cellular networks.

https://eprints.networks.imdea.org/id/document/2488

A Survey on Device-to-Device Communication in Cellular Networks

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.

Decentralized coded caching attains order-optimal memory-rate tradeoff

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.

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 caching algorithm.

Online 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.

Urs Niesen

Papers

Fundamental Limits of Caching

Decentralized coded caching attains order-optimal memory-rate tradeoff

Fundamental Limits of Caching

Online coded caching

Hierarchical Coded Caching