Zipf Distribution

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Andreas F Molisch - One of the best experts on this subject based on the ideXlab platform.

  • optimal throughput outage analysis of cache aided wireless multi hop d2d networks
    IEEE Transactions on Communications, 2021
    Co-Authors: Mingchun Lee, Andreas F Molisch
    Abstract:

    Cache-aided wireless device-to-device (D2D) networks have demonstrated promising performance improvement for video Distribution compared to conventional Distribution methods. Understanding the fundamental scaling behavior of such networks is thus of paramount importance. However, existing scaling laws for multi-hop networks have not been found to be optimal even for the case of Zipf popularity Distributions (gaps between upper and lower bounds are not constants); furthermore, there are no scaling law results for such networks for the more practical case of a Mandelbrot-Zipf (MZipf) popularity Distribution. We thus in this work investigate the throughput-outage performance for cache-aided wireless D2D networks adopting multi-hop communications, with the MZipf popularity Distribution for file requests and users distributed according to Poisson point process. We propose an achievable content caching and delivery scheme and analyze its performance. By showing that the achievable performance is tight to the proposed outer bound, the optimal scaling law is obtained. Furthermore, since the Zipf Distribution is a special case of the MZipf Distribution, the optimal scaling law for the networks considering Zipf popularity Distribution is also obtained, which closes the gap in the literature.

  • scaling behavior for device to device communications with distributed caching
    IEEE Transactions on Information Theory, 2014
    Co-Authors: Negin Golrezaei, Alexandros G Dimakis, Andreas F Molisch
    Abstract:

    We analyze a novel architecture for caching popular video content to enable wireless device-to-device (D2D) collaboration. We focus on the asymptotic scaling characteristics and show how they depend on video content popularity statistics. We identify a fundamental conflict between collaboration distance and interference and show how to optimize the transmission power to maximize frequency reuse. Our main result is a closed form expression of the optimal collaboration distance as a function of the model parameters. Under the common assumption of a Zipf Distribution for content reuse, we show that if the Zipf exponent is greater than 1, it is possible to have a number of D2D interference-free collaboration pairs that scales linearly in the number of nodes. If the Zipf exponent is smaller than 1, we identify the best possible scaling in the number of D2D collaborating links. Surprisingly, a very simple distributed caching policy achieves the optimal scaling behavior.

Mingchun Lee - One of the best experts on this subject based on the ideXlab platform.

  • optimal throughput outage analysis of cache aided wireless multi hop d2d networks
    IEEE Transactions on Communications, 2021
    Co-Authors: Mingchun Lee, Andreas F Molisch
    Abstract:

    Cache-aided wireless device-to-device (D2D) networks have demonstrated promising performance improvement for video Distribution compared to conventional Distribution methods. Understanding the fundamental scaling behavior of such networks is thus of paramount importance. However, existing scaling laws for multi-hop networks have not been found to be optimal even for the case of Zipf popularity Distributions (gaps between upper and lower bounds are not constants); furthermore, there are no scaling law results for such networks for the more practical case of a Mandelbrot-Zipf (MZipf) popularity Distribution. We thus in this work investigate the throughput-outage performance for cache-aided wireless D2D networks adopting multi-hop communications, with the MZipf popularity Distribution for file requests and users distributed according to Poisson point process. We propose an achievable content caching and delivery scheme and analyze its performance. By showing that the achievable performance is tight to the proposed outer bound, the optimal scaling law is obtained. Furthermore, since the Zipf Distribution is a special case of the MZipf Distribution, the optimal scaling law for the networks considering Zipf popularity Distribution is also obtained, which closes the gap in the literature.

Giuseppe Caire - One of the best experts on this subject based on the ideXlab platform.

  • cache induced hierarchical cooperation in wireless device to device caching networks
    IEEE Transactions on Information Theory, 2018
    Co-Authors: An Liu, Vincent K N Lau, Giuseppe Caire
    Abstract:

    We consider a wireless device-to-device caching network where $n$ nodes are placed on a regular grid of area $A\left ({n}\right)$ . Each node caches $L_{C}F$ (coded) bits from a library of size $LF$ bits, where $L$ is the number of files and $F$ is the size of each file. Each node requests a file from the library independently according to a popularity Distribution. Under a commonly used “physical model” and Zipf popularity Distribution, we characterize the optimal per-node capacity scaling law for extended networks (i.e., $A\left ({n}\right)=n$ ). Moreover, we propose a cache-induced hierarchical cooperation scheme and associated cache content placement optimization algorithm to achieve the optimal per-node capacity scaling law. When the path loss exponent $\alpha , the optimal per-node capacity scaling law achieved by the cache-induced hierarchical cooperation can be significantly better than that achieved by the existing state-of-the-art schemes. To the best of our knowledge, this is the first work that completely characterizes the per-node capacity scaling law for wireless caching networks under the physical model and Zipf Distribution with an arbitrary skewness parameter $\tau $ . While scaling law analysis yields clean results, it may not accurately reflect the throughput performance of a large network with a finite number of nodes. Therefore, we also analyze the throughput of the proposed cache-induced hierarchical cooperation for networks of practical size. The analysis and simulations verify that cache-induced hierarchical cooperation can also achieve a large throughput gain over the cache-assisted multihop scheme for networks of practical size.

  • cache induced hierarchical cooperation in wireless device to device caching networks
    arXiv: Information Theory, 2016
    Co-Authors: An Liu, Vincent K N Lau, Giuseppe Caire
    Abstract:

    We consider a wireless device-to-device (D2D) caching network where n nodes are placed on a regular grid of area A(n). Each node caches L_C*F (coded) bits from a library of size L*F bits, where L is the number of files and F is the size of each file. Each node requests a file from the library independently according to a popularity Distribution. Under a commonly used "physical model" and Zipf popularity Distribution, we characterize the optimal per-node capacity scaling law for extended networks (i.e., A(n). Moreover, we propose a cache-induced hierarchical cooperation scheme and associated cache content placement optimization algorithm to achieve the optimal per-node capacity scaling law. When the path loss exponent \alpha<3, the optimal per-node capacity scaling law achieved by the cache-induced hierarchical cooperation can be significantly better than that achieved by the existing state-of-the-art schemes. To the best of our knowledge, this is the first work that completely characterizes the per-node capacity scaling law for wireless caching networks under the physical model and Zipf Distribution with an arbitrary skewness parameter \tau. While scaling law analysis yields clean results, it may not accurately reflect the throughput performance of a large network with a finite number of nodes. Therefore, we also analyze the throughput of the proposed cache-induced hierarchical cooperation for networks of practical size. The analysis and simulations verify that cache-induced hierarchical cooperation can also achieve a large throughput gain over the cache-assisted multihop scheme for networks of practical size.

Robert L Axtell - One of the best experts on this subject based on the ideXlab platform.

  • Zipf Distribution of u s firm sizes
    Social Science Research Network, 2001
    Co-Authors: Robert L Axtell
    Abstract:

    Analyses of firm sizes have historically used data that included limited samples of small firms, data typically described by lognormal Distributions. Using data on the entire population of tax-paying firms in the United States, I show here that the Zipf Distribution characterizes firm sizes: the probability a firm is larger than size s is inversely proportional to s. These results hold for data from multiple years and for various definitions of firm size.

An Liu - One of the best experts on this subject based on the ideXlab platform.

  • cache induced hierarchical cooperation in wireless device to device caching networks
    IEEE Transactions on Information Theory, 2018
    Co-Authors: An Liu, Vincent K N Lau, Giuseppe Caire
    Abstract:

    We consider a wireless device-to-device caching network where $n$ nodes are placed on a regular grid of area $A\left ({n}\right)$ . Each node caches $L_{C}F$ (coded) bits from a library of size $LF$ bits, where $L$ is the number of files and $F$ is the size of each file. Each node requests a file from the library independently according to a popularity Distribution. Under a commonly used “physical model” and Zipf popularity Distribution, we characterize the optimal per-node capacity scaling law for extended networks (i.e., $A\left ({n}\right)=n$ ). Moreover, we propose a cache-induced hierarchical cooperation scheme and associated cache content placement optimization algorithm to achieve the optimal per-node capacity scaling law. When the path loss exponent $\alpha , the optimal per-node capacity scaling law achieved by the cache-induced hierarchical cooperation can be significantly better than that achieved by the existing state-of-the-art schemes. To the best of our knowledge, this is the first work that completely characterizes the per-node capacity scaling law for wireless caching networks under the physical model and Zipf Distribution with an arbitrary skewness parameter $\tau $ . While scaling law analysis yields clean results, it may not accurately reflect the throughput performance of a large network with a finite number of nodes. Therefore, we also analyze the throughput of the proposed cache-induced hierarchical cooperation for networks of practical size. The analysis and simulations verify that cache-induced hierarchical cooperation can also achieve a large throughput gain over the cache-assisted multihop scheme for networks of practical size.

  • cache induced hierarchical cooperation in wireless device to device caching networks
    arXiv: Information Theory, 2016
    Co-Authors: An Liu, Vincent K N Lau, Giuseppe Caire
    Abstract:

    We consider a wireless device-to-device (D2D) caching network where n nodes are placed on a regular grid of area A(n). Each node caches L_C*F (coded) bits from a library of size L*F bits, where L is the number of files and F is the size of each file. Each node requests a file from the library independently according to a popularity Distribution. Under a commonly used "physical model" and Zipf popularity Distribution, we characterize the optimal per-node capacity scaling law for extended networks (i.e., A(n). Moreover, we propose a cache-induced hierarchical cooperation scheme and associated cache content placement optimization algorithm to achieve the optimal per-node capacity scaling law. When the path loss exponent \alpha<3, the optimal per-node capacity scaling law achieved by the cache-induced hierarchical cooperation can be significantly better than that achieved by the existing state-of-the-art schemes. To the best of our knowledge, this is the first work that completely characterizes the per-node capacity scaling law for wireless caching networks under the physical model and Zipf Distribution with an arbitrary skewness parameter \tau. While scaling law analysis yields clean results, it may not accurately reflect the throughput performance of a large network with a finite number of nodes. Therefore, we also analyze the throughput of the proposed cache-induced hierarchical cooperation for networks of practical size. The analysis and simulations verify that cache-induced hierarchical cooperation can also achieve a large throughput gain over the cache-assisted multihop scheme for networks of practical size.