We show that the 2x2x2 interference channel, i.e., the multihop interference channel formed by concatenation of two 2-user interference channels achieves the min-cut outer bound value of 2 DoF, for almost all values of channel coefficients, for both time-varying or fixed channel coefficients. The key to this result is a new idea, called aligned interference neutralization, that provides a way to align interference terms over each hop in a manner that allows them to be cancelled over the air at the last hop.
The degrees of freedom (DoF) region is characterized for the $2$-user multiple input multiple output (MIMO) broadcast channel (BC), where the transmitter is equipped with $M$ antennas, the two receivers are equipped with $N_1$ and $N_2$ antennas, and the levels of channel state information at the transmitter (CSIT) for the two users are parameterized by $β_1, β_2$, respectively. The achievability of the DoF region was established by Hao, Rassouli and Clerckx, but no proof of optimality was heretofore available. The proof of optimality is provided in this work with the aid of sum-set inequaliti…
Degrees of Freedom for Instantaneous-Relay Aided Interference Channel: Bounds and Achievable Schemes
研究了具有J个瞬时中继的K用户平坦衰落MIMO干扰信道。在KICJR中，包括中继在内的信源和信宿之间的有效信道具有一定的结构，并且是非通用的。对于非通用信道，可实现的自由度（DoF）仍然是未知的。Lee和Wang表明，通过使用对准干扰中和方案，在2 IC IR系统中可实现3/2自由度，这比2用户干扰信道多50%。但文献中没有研究其他KICJR网络的自由度性能和可实现的方案。在本文中，我们设计了一个可实现的方案，称为限制干扰对齐瞬时中继辅助干扰信道。此外，找到见解的最大可实现的自由度自由度，我们开发线性波束形成的基础上的均方误差（MSE）最小化作为一个可实现的计划。通过对干涉对准方程组正确性的研究，给出了干涉对准系统最大可达自由度的上界。数值结果表明，所提出的限制性干扰对齐方案和基于MSE的波束形成的自由度性能匹配的干扰对齐方程的适当性所确定的上界。
This work investigates the degrees of freedom (DoF) of a downlink cache-aided cellular network where the locations of base stations (BSs) are modeled as a grid topology and users within a grid cell can only communicate with four nearby BSs. We adopt a cache placement method with uncoded prefetching tailored for the network with partial connectivity. According to the overlapped degree of cached contents among BSs, we propose transmission schemes with no BS cooperation, partial BS cooperation, and full BS cooperation, respectively, for different cache sizes. In specific, the common cached conten…
Aligned-Images Sumset Inequalities are used in this work to study the Generalized Degrees of Freedom (GDoF) of the symmetric layered multi-hop interference channel under the robust assumption that the channel state information at the transmitters (CSIT) is limited to finite precision. First, the sum-GDoF value is characterized for the $2\times 2\times 2$ setting that is comprised of $2$ sources, $2$ relays, and $2$ destinations. It is shown that the sum-GDoF do not improve even if perfect CSIT is allowed in the first hop, as long as the CSIT in the second hop is limited to finite precision. Th…
Aligned Image Sets under Channel Uncertainty: Settling a Conjecture by Lapidoth, Shamai and Wigger on the Collapse of Degrees of Freedom under Finite Precision CSIT
In this paper, we propose a signal-aligned network coding (SNC) scheme for K-user time-varying multiple-input multiple-output (MIMO) interference channels with limited receiver cooperation. We assume that the receivers are connected to a central processor via wired cooperation links with individual limited capacities. Our SNC scheme determines the precoding matrices of the transmitters so that the transmitted signals are aligned at each receiver. The aligned signals are then decoded into noiseless integer combinations of messages, also known as network-coded messages, by physical-layer network…
We study the $K$-user, $M$-subchannel parallel multiple-input-single-output (MISO) broadcast channel (BC) under arbitrary levels of partial channel state information at the transmitter (CSIT). We show that the parallel subchannels constituting this setting are separable from a degrees-of-freedom (DoF) region perspective if and only if the partial CSIT pattern is totally ordered. This total order condition corresponds to users abiding by the same order, with respect to their CSIT quality levels, in each of the parallel subchannels. For instance, let $α_{k}^{[l]}$ and $α_{j}^{[l]}$ be the CSIT q…
The Generalized Degrees of Freedom (GDoF) of the two user interference channel are characterized for all parameter regimes under the assumption of finite precision channel state information at the transmitters (CSIT), when a limited amount of (half-duplex or full-duplex) cooperation is allowed between the transmitters in the form of $π$ DoF of shared messages. In all cases, the number of over-the-air bits that each cooperation bit buys is shown to be equal to either $0, 1, 1/2$ or $1/3$. The most interesting aspect of the result is the $1/3$ slope, which appears only under finite precision CSI…
In this work, we study the generalized degrees-of-freedom (GDoF) of downlink and uplink cellular networks, modeled as Gaussian interfering broadcast channels (IBC) and Gaussian interfering multiple access channels (IMAC), respectively. We focus on regimes of low inter-cell interference, where single-cell transmission with power control and treating inter-cell interference as noise (mc-TIN) is GDoF optimal. Recent works have identified two relevant regimes in this context: one in which the GDoF region achieved through mc-TIN for both the IBC and IMAC is a convex polyhedron without the need for …
