Kangqi Liu

Fundamental Tradeoff Between Storage and Latency in Cache-Aided Wireless Interference Networks

This paper studies the fundamental tradeoff between storage and latency in a general wireless interference network with caches equipped at all transmitters and receivers. The tradeoff is characterized by an information-theoretic metric, normalized delivery time (NDT), which is the worst case delivery time of the actual traffic load at a transmission rate specified by degrees of freedom of a given channel. We obtain both an achievable upper bound and a theoretical lower bound of the minimum NDT for any number of transmitters, any number of receivers, and any feasible cache size tuple. We show that the achievable NDT is exactly optimal in certain cache size regions, and is within a bounded multiplicative gap to the theoretical lower bound in other regions. In the achievability analysis, we first propose a novel cooperative transmitter/receiver coded caching strategy. It offers the freedom to adjust file splitting ratios for NDT minimization. We then propose a delivery strategy that transforms the considered interference network into a new class of cooperative X-multicast channels. It leverages local caching gain, coded multicasting gain, and transmitter cooperation gain (via interference alignment and interference neutralization) opportunistically. Finally, the achievable NDT is obtained by solving a linear programming problem. This paper reveals that with caching at both transmitter and receiver sides, the network can benefit simultaneously from traffic load reduction and transmission rate enhancement, thereby effectively reducing the content delivery latency.

Generalized Signal Alignment: On the Achievable DoF for Multi-User MIMO Two-Way Relay Channels

This paper studies the achievable degrees of freedom (DoF) for multi-user multiple-input multiple-output (MIMO) two-way relay channels, where there are K source nodes, each equipped with M antennas, one relay node, equipped with N antennas, and each source node exchanges independent messages with an arbitrary set of other source nodes via the relay. By allowing an arbitrary information exchange pattern, the considered channel model is a unified one. It includes several existing channel models as special cases: 1) K-user MIMO Y channel; 2) multi-pair MIMO two-way relay channel; 3) generalized MIMO two-way X relay channel; and 4) L-cluster MIMO multiway relay channel. Previous studies mainly considered the achievability of the DoF cut-set bound 2N at the antenna configuration N <; 2M by applying signal alignment for network coding. This paper aims to investigate the achievability of the DoF cut-set bound K M for the case N 2M. To this end, we first derive tighter DoF upper bounds for three special cases of the considered channel model. Then, we propose a new transmission framework, generalized signal alignment (GSA), to approach these bounds. The notion of GSA is to form network-coded symbols by aligning every pair of signals to be exchanged in a compressed subspace at the relay. A necessary and sufficient condition to construct the relay compression matrix is given. We show that using GSA, the new DoF upper bound is achievable when: 1) N/m ∈ (0, 2+ 4/{K(K-1)}]∪[K-2, +∞) for the K-user MIMO Y channel; 2) N/M ∈ (0,2 +4/K]∪[K - 2, +∞) for the multi-pair MIMO two-way relay channel; and 3) N/M ∈ (0, 2+ 8/K2]∪[K-2, +∞) for the generalized MIMO two-way X relay channel. We also provide the antenna configuration regions for the general multi-user MIMO two-way relay channel to achieve the total DoF KM.

Cooperative Tx/Rx caching in interference channels: A storage-latency tradeoff study

This paper studies the storage-latency tradeoff in the 3 × 3 wireless interference network with caches equipped at all transmitters and receivers. The tradeoff is characterized by the so-called fractional delivery time (FDT) at given normalized transmitter and receiver cache sizes. We first propose a generic cooperative transmitter/receiver caching strategy with adjustable file splitting ratios. Based on this caching strategy, we then design the delivery phase carefully to turn the considered interference channel opportunistically into broadcast channel, multicast channel, X channel, or a hybrid form of these channels. After that, we obtain an achievable upper bound of the minimum FDT by solving a linear programming problem of the file splitting ratios. The achievable FDT is a convex and piece-wise linear decreasing function of the cache sizes. Receiver local caching gain, coded multicasting gain, and transmitter cooperation gain (interference alignment and interference neutralization) are leveraged in different cache size regions.

Generalized signal alignment for arbitrary MIMO two-way relay channels

In this paper, we study the achievable degrees of freedom (DoF) for an arbitrary MIMO two-way relay channel, where there are K source nodes, each equipped with M_i antennas, for i = 1, 2, ⋯, K, and one relay node, equipped with N antennas. Each source node can exchange independent messages with an arbitrary set of other source nodes assisted by the relay. We extend our newly-proposed transmission scheme, generalized signal alignment (GSA) in [1], to the arbitrary MIMO two-way relay channel with antenna configuration satisfying N ≥ M_i + M_j, ∀i ≠ j. The notion of GSA is to form network-coded symbols by aligning every pair of signals to be exchanged in a projected subspace at the relay. This is realized by jointly designing the precoding matrices at all source nodes and the processing matrix at the relay node. Moreover, the aligned subspaces are orthogonal to each other. Applying the GSA, we show that the DoF upper bound min {Σ_i=1^K M_{i, 2} Σ_i=2^K M_i, 2N} is tight under the antenna configuration N ≥ max{Σ_i=1^K M_i-M_s-M_t+d_{s, t} | ∀_s, t}. Here, d_{s, t} denotes the DoF of the message exchanged between nodes s and t. In the special case when the arbitrary MIMO two-way relay channel reduces to the K-user MIMO Y channel, we show that our achievable region of DoF upper bound with GSA is larger than the existing result.

Generalized signal alignment for MIMO two-way X relay channels

We study the degrees of freedom (DoF) of MIMO two-way X relay channels. Previous work studied the case N <; 2M, where N and M denote the number of antennas at the relay and each source, respectively, and showed that the maximum DoF of 2N is achievable when N <; ⌊8M/5⌋ by applying signal alignment (SA) for network coding and interference cancelation. This work considers the case N > 2M where the performance is limited by the number of antennas at each source node and conventional SA is not feasible. We propose a generalized signal alignment (GSA) based transmission scheme. The key is to let the signals to be exchanged between every source node align in a transformed subspace, rather than the direct subspace, at the relay so as to form network-coded signals. This is realized by jointly designing the precoding matrices at all source nodes and the processing matrix at the relay. Moreover, the aligned subspaces are orthogonal to each other. By applying the GSA, we show that the DoF upper bound 4M is achievable when M ≤ ⌊ 2N/5 ⌋ (M is even) or M ≤ ⌊ 2N-1 /5 ⌋ (M is odd). Numerical results also demonstrate that our proposed transmission scheme is feasible and effective.

An efficient beamforming scheme for generalized MIMO two-way X relay channels

Recently, a multiple-input multiple-output (MIMO) two-way X relay channel, where two groups of source nodes each having 2 nodes exchange independent messages via a common relay node, was studied in [1]. In this paper, we extend it to the generalized MIMO two-way X relay channel, where m ≥ 2 and n ≥ 2 source nodes are contained in two groups, respectively. Based on signal space alignment, a new beamforming scheme is proposed to maximize the minimum effective signal to interference plus noise ratios (SINRs) among all data streams. The beamforming vectors are designed by an iterative algorithm in which a closed-form solution is obtained in each step. Moreover, we show that the power allocation problem given the shape of the beamformers can be transformed as a linear programming problem. Simulation results show that the proposed beamforming scheme can achieve significantly better error performance than random beamforming schemes subject to signal space alignment only.

A Storage-Latency Tradeoff Study for Cache-Aided MIMO Interference Networks

Caching is an effective technique to improve user perceived experience for massive content delivery in wireless networks. An essential problem in cache-aided wireless networks is to find what and how much gain can be achieved by caching. This paper provides a study of the fundamental storage- latency tradeoff for a cache-aided MIMO interference network with 3 transmitters and 3 receivers and each node equipped with

On the sum DoF of the asymmetric four-user MIMO Y channel

M

Optimal Degrees of Freedom Region for the Asymmetric MIMO Y Channel

antennas. By using a newly proposed novel file splitting and caching strategy, the network topology during the content delivery phase is turned opportunistically to MIMO X channel, MIMO broadcast channel, MIMO multicast channel, or a hybrid form of these channels. Linear-precoding based interference management schemes such as interference alignment and neutralization over finite symbol extension are designed for these channels. We characterize the storage-latency tradeoff by \emph{fractional delivery time} (FDT), a metric to evaluate the worst-case delivery time of the actual traffic load at a rate specified by the degrees of freedom (DoF) of the considered channel. The achievable FDT of our proposed scheme decreases piecewise linearly with the normalized cache sizes and is inversely proportional to the number of antennas. It is also shown that the achievable FDT is optimal at certain cache size regions and is within a multiplicative gap of 2 from the optimum at other regions.

A new DoF upper bound and its achievability for K-user MIMO Y channels

This work studies the sum degrees of freedom (DoF) of the asymmetric four-user MIMO Y channel, where each user i, for 1 ≤ i ≤ 4, is equipped with Mi antennas, and the relay is equipped with N antennas. By using the genie message approach, we derive that the sum DoF is upper bounded by min {Σ_i=1⁴ M_i, 2 Σ_i=2⁴ M_i, 2N, 2/7 Σ_∀i,∀j>i max{N, M_i + M_j} }, where M₁ ≥ M₂ ≥ M₃ ≥ M₄. Then, we show that the bound is tight under certain antenna constraints using signal alignment, generalized signal alignment, and antenna deactivation techniques.