The work establishes the exact performance limits of stochastic coded caching when users share a ... more The work establishes the exact performance limits of stochastic coded caching when users share a bounded number of cache states, and when the association between users and caches, is random. Under the premise that more balanced user-to-cache associations perform better than unbalanced ones, our work provides a statistical analysis of the average performance of such networks, identifying in closed form, the exact optimal average delivery time. To insightfully capture this delay, we derive easy to compute closed-form analytical bounds that prove tight in the limit of a large number Λ of cache states. In the scenario where delivery involves K users, we conclude that the multiplicative performance deterioration due to randomness – as compared to the well-known deterministic uniform case – can be unbounded and can scale as Θ( logΛ/loglogΛ) at K=Θ(Λ), and that this scaling vanishes when K=Ω(ΛlogΛ). To alleviate this adverse effect of cache-load imbalance, we consider various load balancin...
This work presents a new way of exploiting nonuniform file popularity in coded caching networks. ... more This work presents a new way of exploiting nonuniform file popularity in coded caching networks. Focusing on a fully-connected fully-interfering wireless setting with multiple cache-enabled transmitters and receivers, we show how nonuniform file popularity can be used very efficiently to accelerate the impact of transmitter-side data redundancy on receiverside coded caching. This approach is motivated by the recent discovery that, under any realistic file-size constraint, having content appear in multiple transmitters can in fact dramatically boost the speed-up factor attributed to coded caching. We formulate an optimization problem that exploits file popularity to optimize the placement of files at the transmitters. We then provide a proof that reduces significantly the variable search space, and propose a new search algorithm that solves the problem at hand. We also prove an analytical performance upper bound, which is in fact met by our algorithm in the regime of many receivers. ...
We investigate the decoding delay performance of a communication network in which a single source... more We investigate the decoding delay performance of a communication network in which a single source is transmitting data packets to a single receiver via multiple routers. Network coding is applied to all data packets at the source at each transmission opportunity. Receiver receives network coded packets from routers and decodes them. We define the delay as the time between arrival of a data packet at the source and decoding of all the packets served in the busy period of the source queue starting from the arrival of that data packet. We show that the delay can be expressed in closed-form.
2020 18th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOPT), 2020
The work presents a new way of exploiting non-uniform file popularity in caching networks. Focusi... more The work presents a new way of exploiting non-uniform file popularity in caching networks. Focusing on the interference channel with cache-enabled transmitters and receivers, we show how non-uniform file popularity can be used to accelerate the impact of transmitter-side data redundancy in coded caching. This approach is motivated by the recent discovery that under realistic file-size constraints, having content appear in multiple transmitters can boost multiplicatively the speed-up factor attributed to coded caching.We formulate the problem through an optimization algorithm, which seeks to optimize the number of transmitters each file is cached at, as a function of that file’s popularity. Part of the optimization effort involves a biconvex problem; such problems are traditionally solved by heuristic Alternate Convex Search methods that generally do not guarantee the global optimum. To avoid this, we follow a more involved path which includes the design of a new search algorithm tha...
The work establishes the exact fundamental limits of stochastic coded caching when users share a ... more The work establishes the exact fundamental limits of stochastic coded caching when users share a bounded number of cache states, and when the association between users and caches, is random. This association can greatly affect performance, which improves when the association is more balanced across the caches, and which deteriorates when this association becomes less uniform. Our work provides a statistical analysis of the average performance of such networks, quantifying the effect of randomness by identifying in closed-form, the exact optimal average delivery time. To insightfully capture this delay, we derive the exact scaling laws of the optimal average delivery time. In the scenario where delivery involves $K$ users, we conclude that the multiplicative performance deterioration due to randomness - as compared to the well-known deterministic uniform case - can be unbounded and can scale as $\Theta\left(\frac{\log\Lambda}{\log\log\Lambda}\right)$ at $K=\Theta(\Lambda)$, and that ...
The work establishes the exact performance limits of stochastic coded caching when users share a ... more The work establishes the exact performance limits of stochastic coded caching when users share a bounded number of cache states, and when the association between users and caches, is random. Under the premise that more balanced user-to-cache associations perform better than unbalanced ones, our work provides a statistical analysis of the average performance of such networks, identifying in closed form, the exact optimal average delivery time. To insightfully capture this delay, we derive easy to compute closed-form analytical bounds that prove tight in the limit of a large number $\Lambda$ of cache states. In the scenario where delivery involves $K$ users, we conclude that the multiplicative performance deterioration due to randomness -- as compared to the well-known deterministic uniform case -- can be unbounded and can scale as $\Theta\left( \frac{\log \Lambda}{\log \log \Lambda} \right)$ at $K=\Theta\left(\Lambda\right)$, and that this scaling vanishes when $K=\Omega\left(\Lambda...
2017 IEEE Wireless Communications and Networking Conference (WCNC), 2017
In this work we investigate optimal geographical caching in heterogeneous cellular networks where... more In this work we investigate optimal geographical caching in heterogeneous cellular networks where different types of base stations (BSs) have different cache capacities. Users request files from a content library according to a known probability distribution. The performance metric is the total hit probability, which is the probability that a user at an arbitrary location in the plane will find the content that it requires in one of the BSs that it is covered by. We consider the problem of optimally placing content in all BSs jointly. As this problem is not convex, we provide a heuristic scheme by finding the optimal placement policy for one type of base station conditioned on the placement in all other types. We demonstrate that these individual optimization problems are convex and we provide an analytical solution. As an illustration, we find the optimal placement policy of the small base stations (SBSs) depending on the placement policy of the macro base stations (MBSs). We show ...
We investigate optimal geographical caching in heterogeneous cellular networks, where different t... more We investigate optimal geographical caching in heterogeneous cellular networks, where different types of base stations (BSs) have different cache capacities. The content library contains files with different popularities. The performance metric is the total hit probability. The problem of optimally placing content in all BSs jointly is not convex in general. However, we show that when BSs are deployed according to homogeneous Poisson point processes (PPP), independently for each type, we can formulate the problem as a convex problem. We give the optimal solution to the joint problem for the PPP deployment. For the general case, we provide a distributed local optimization algorithm (LOA) that finds the optimal placement policies for different types of BSs. We find the optimal placement policy of the small BSs (SBSs) depending on the placement policy of the macro BSs (MBSs). We show that storing the most popular content in the MBSs is almost optimal if the SBSs are using optimal place...
2012 IEEE 13th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 2012
ABSTRACT In this paper, polarization performance of polar code generator matrices is analyzed. We... more ABSTRACT In this paper, polarization performance of polar code generator matrices is analyzed. We obtain the Bhattacharyya parameters of polarized channels generated by all possible lower-triangular 3 × 3 generator matrices and evaluate the corresponding polarization behavior of polar coded systems via both asymptotical polarization rate exponents and finite-length polarization distance graphs. A ranking of all lower-triangular 3 × 3 generator matrices is also provided.
ABSTRACT Polar coding is a recently proposed coding technique that can provably achieve the chann... more ABSTRACT Polar coding is a recently proposed coding technique that can provably achieve the channel capacity. The polar code structure, which is based on the original 2 × 2 generator matrix, polarises the channels, that is, a portion of the channel capacities approach 1, whereas the remaining channel capacities approach 0. Owing to the specific size of this original generator matrix, polar codes can only have code lengths equal to the powers of 2, resulting in inefficiency for codes of practical lengths. In this study, the performance of finite-length polar codes over the binary erasure channel is analysed. A normalised polarisation distance measure is defined and polar codes from different generator matrices showing different amount of polarisation are compared using this measure. Encoding structures for these generalised polar codes are proposed and polarisation performances in both asymptotical and finite-length cases are investigated for generator matrices of size 3 × 3 and 4 × 4. A generalised decoder is also proposed for this generator matrix and its erasure rate is compared with that of the original generator matrix. It is shown that polar codes that have performance similar to the original construction can be constructed and used for a variety of code lengths, not necessarily equal to powers of 2, using generalised generator matrices.
2012 20th Signal Processing and Communications Applications Conference (SIU), 2012
In this paper, the effects of the generator matrix selection on the polarization performance of p... more In this paper, the effects of the generator matrix selection on the polarization performance of polar coded communication systems is analyzed. We consider the problem of calculating the Bhattacharyya parameters for generator matrices of size larger than the standard size 2 × 2 and demonstrate that it is not an easy task to obtain the channel capacities in a recursive
The work establishes the exact performance limits of stochastic coded caching when users share a ... more The work establishes the exact performance limits of stochastic coded caching when users share a bounded number of cache states, and when the association between users and caches, is random. Under the premise that more balanced user-to-cache associations perform better than unbalanced ones, our work provides a statistical analysis of the average performance of such networks, identifying in closed form, the exact optimal average delivery time. To insightfully capture this delay, we derive easy to compute closed-form analytical bounds that prove tight in the limit of a large number Λ of cache states. In the scenario where delivery involves K users, we conclude that the multiplicative performance deterioration due to randomness – as compared to the well-known deterministic uniform case – can be unbounded and can scale as Θ( logΛ/loglogΛ) at K=Θ(Λ), and that this scaling vanishes when K=Ω(ΛlogΛ). To alleviate this adverse effect of cache-load imbalance, we consider various load balancin...
This work presents a new way of exploiting nonuniform file popularity in coded caching networks. ... more This work presents a new way of exploiting nonuniform file popularity in coded caching networks. Focusing on a fully-connected fully-interfering wireless setting with multiple cache-enabled transmitters and receivers, we show how nonuniform file popularity can be used very efficiently to accelerate the impact of transmitter-side data redundancy on receiverside coded caching. This approach is motivated by the recent discovery that, under any realistic file-size constraint, having content appear in multiple transmitters can in fact dramatically boost the speed-up factor attributed to coded caching. We formulate an optimization problem that exploits file popularity to optimize the placement of files at the transmitters. We then provide a proof that reduces significantly the variable search space, and propose a new search algorithm that solves the problem at hand. We also prove an analytical performance upper bound, which is in fact met by our algorithm in the regime of many receivers. ...
We investigate the decoding delay performance of a communication network in which a single source... more We investigate the decoding delay performance of a communication network in which a single source is transmitting data packets to a single receiver via multiple routers. Network coding is applied to all data packets at the source at each transmission opportunity. Receiver receives network coded packets from routers and decodes them. We define the delay as the time between arrival of a data packet at the source and decoding of all the packets served in the busy period of the source queue starting from the arrival of that data packet. We show that the delay can be expressed in closed-form.
2020 18th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOPT), 2020
The work presents a new way of exploiting non-uniform file popularity in caching networks. Focusi... more The work presents a new way of exploiting non-uniform file popularity in caching networks. Focusing on the interference channel with cache-enabled transmitters and receivers, we show how non-uniform file popularity can be used to accelerate the impact of transmitter-side data redundancy in coded caching. This approach is motivated by the recent discovery that under realistic file-size constraints, having content appear in multiple transmitters can boost multiplicatively the speed-up factor attributed to coded caching.We formulate the problem through an optimization algorithm, which seeks to optimize the number of transmitters each file is cached at, as a function of that file’s popularity. Part of the optimization effort involves a biconvex problem; such problems are traditionally solved by heuristic Alternate Convex Search methods that generally do not guarantee the global optimum. To avoid this, we follow a more involved path which includes the design of a new search algorithm tha...
The work establishes the exact fundamental limits of stochastic coded caching when users share a ... more The work establishes the exact fundamental limits of stochastic coded caching when users share a bounded number of cache states, and when the association between users and caches, is random. This association can greatly affect performance, which improves when the association is more balanced across the caches, and which deteriorates when this association becomes less uniform. Our work provides a statistical analysis of the average performance of such networks, quantifying the effect of randomness by identifying in closed-form, the exact optimal average delivery time. To insightfully capture this delay, we derive the exact scaling laws of the optimal average delivery time. In the scenario where delivery involves $K$ users, we conclude that the multiplicative performance deterioration due to randomness - as compared to the well-known deterministic uniform case - can be unbounded and can scale as $\Theta\left(\frac{\log\Lambda}{\log\log\Lambda}\right)$ at $K=\Theta(\Lambda)$, and that ...
The work establishes the exact performance limits of stochastic coded caching when users share a ... more The work establishes the exact performance limits of stochastic coded caching when users share a bounded number of cache states, and when the association between users and caches, is random. Under the premise that more balanced user-to-cache associations perform better than unbalanced ones, our work provides a statistical analysis of the average performance of such networks, identifying in closed form, the exact optimal average delivery time. To insightfully capture this delay, we derive easy to compute closed-form analytical bounds that prove tight in the limit of a large number $\Lambda$ of cache states. In the scenario where delivery involves $K$ users, we conclude that the multiplicative performance deterioration due to randomness -- as compared to the well-known deterministic uniform case -- can be unbounded and can scale as $\Theta\left( \frac{\log \Lambda}{\log \log \Lambda} \right)$ at $K=\Theta\left(\Lambda\right)$, and that this scaling vanishes when $K=\Omega\left(\Lambda...
2017 IEEE Wireless Communications and Networking Conference (WCNC), 2017
In this work we investigate optimal geographical caching in heterogeneous cellular networks where... more In this work we investigate optimal geographical caching in heterogeneous cellular networks where different types of base stations (BSs) have different cache capacities. Users request files from a content library according to a known probability distribution. The performance metric is the total hit probability, which is the probability that a user at an arbitrary location in the plane will find the content that it requires in one of the BSs that it is covered by. We consider the problem of optimally placing content in all BSs jointly. As this problem is not convex, we provide a heuristic scheme by finding the optimal placement policy for one type of base station conditioned on the placement in all other types. We demonstrate that these individual optimization problems are convex and we provide an analytical solution. As an illustration, we find the optimal placement policy of the small base stations (SBSs) depending on the placement policy of the macro base stations (MBSs). We show ...
We investigate optimal geographical caching in heterogeneous cellular networks, where different t... more We investigate optimal geographical caching in heterogeneous cellular networks, where different types of base stations (BSs) have different cache capacities. The content library contains files with different popularities. The performance metric is the total hit probability. The problem of optimally placing content in all BSs jointly is not convex in general. However, we show that when BSs are deployed according to homogeneous Poisson point processes (PPP), independently for each type, we can formulate the problem as a convex problem. We give the optimal solution to the joint problem for the PPP deployment. For the general case, we provide a distributed local optimization algorithm (LOA) that finds the optimal placement policies for different types of BSs. We find the optimal placement policy of the small BSs (SBSs) depending on the placement policy of the macro BSs (MBSs). We show that storing the most popular content in the MBSs is almost optimal if the SBSs are using optimal place...
2012 IEEE 13th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 2012
ABSTRACT In this paper, polarization performance of polar code generator matrices is analyzed. We... more ABSTRACT In this paper, polarization performance of polar code generator matrices is analyzed. We obtain the Bhattacharyya parameters of polarized channels generated by all possible lower-triangular 3 × 3 generator matrices and evaluate the corresponding polarization behavior of polar coded systems via both asymptotical polarization rate exponents and finite-length polarization distance graphs. A ranking of all lower-triangular 3 × 3 generator matrices is also provided.
ABSTRACT Polar coding is a recently proposed coding technique that can provably achieve the chann... more ABSTRACT Polar coding is a recently proposed coding technique that can provably achieve the channel capacity. The polar code structure, which is based on the original 2 × 2 generator matrix, polarises the channels, that is, a portion of the channel capacities approach 1, whereas the remaining channel capacities approach 0. Owing to the specific size of this original generator matrix, polar codes can only have code lengths equal to the powers of 2, resulting in inefficiency for codes of practical lengths. In this study, the performance of finite-length polar codes over the binary erasure channel is analysed. A normalised polarisation distance measure is defined and polar codes from different generator matrices showing different amount of polarisation are compared using this measure. Encoding structures for these generalised polar codes are proposed and polarisation performances in both asymptotical and finite-length cases are investigated for generator matrices of size 3 × 3 and 4 × 4. A generalised decoder is also proposed for this generator matrix and its erasure rate is compared with that of the original generator matrix. It is shown that polar codes that have performance similar to the original construction can be constructed and used for a variety of code lengths, not necessarily equal to powers of 2, using generalised generator matrices.
2012 20th Signal Processing and Communications Applications Conference (SIU), 2012
In this paper, the effects of the generator matrix selection on the polarization performance of p... more In this paper, the effects of the generator matrix selection on the polarization performance of polar coded communication systems is analyzed. We consider the problem of calculating the Bhattacharyya parameters for generator matrices of size larger than the standard size 2 × 2 and demonstrate that it is not an easy task to obtain the channel capacities in a recursive
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