Integer-forcing in multiterminal coding: uplink-downlink duality and source-channel duality

Interference is considered to be a major obstacle to wireless communication. Popular approaches, such as the zero-forcing receiver in MIMO (multiple-input and multiple-output) multiple-access channel (MAC) and zero-forcing (ZF) beamforming in MIMO broadcast channel (BC), eliminate the interference first and decode each codeword separately using a conventional single-user decoder. Recently, a transceiver architecture called integer-forcing (IF) has been proposed in the context of the MIMO Gaussian multiple-access channel to exploit integer-linear combinations of the codewords. Instead of treating other codewords as interference, the integer-forcing approach decodes linear combinations of the codewords from different users and solves for desired codewords. Integer-forcing can closely approach the performance of the optimal joint maximum likelihood decoder. An advanced version called successive integer-forcing can achieve the sum capacity of the MIMO MAC channel. Several extensions of integer-forcing have been developed in various scenarios, such as integer-forcing for the Gaussian MIMO broadcast channel, integer-forcing for Gaussian distributed source coding and integer-forcing interference alignment for the Gaussian interference channel. This dissertation demonstrates duality relationships for integer-forcing among three different channel models. We explore in detail two distinct duality types in this thesis: uplink-downlink duality and source-channel duality. Uplink-downlink duality is established for integer-forcing between the Gaussian MIMO multiple-access channel and its dual Gaussian MIMO broadcast channel. We show that under a total power constraint, integer-forcing can achieve the same sum rate in both cases. We further develop a dirty-paper integer-forcing scheme for the Gaussian MIMO BC and show an uplink-downlink duality with successive integer-forcing for the Gaussian MIMO MAC. The source-channel duality is established for integer-forcing between the Gaussian MIMO multiple-access channel and its dual Gaussian distributed source coding problem. We extend previous results for integer-forcing source coding to allow for successive cancellation. For integer-forcing without successive cancellation in both channel coding and source coding, we show the rates in two scenarios lie within a constant gap of one another. We further show that there exists a successive cancellation scheme such that both integer-forcing channel coding and integer-forcing source coding achieve the same rate tuple

Integer-forcing architectures: cloud-radio access networks, time-variation and interference alignment

Next-generation wireless communication systems will need to contend with many active mobile devices, each of which will require a very high data rate. To cope with this growing demand, network deployments are becoming denser, leading to higher interference between active users. Conventional architectures aim to mitigate this interference through careful design of signaling and scheduling protocols. Unfortunately, these methods become less effective as the device density increases. One promising option is to enable cellular basestations (i.e., cell towers) to jointly process their received signals for decoding users’ data packets as well as to jointly encode their data packets to the users. This joint processing architecture is often enabled by a cloud radio access network that links the basestations to a central processing unit via dedicated connections. One of the main contributions of this thesis is a novel end-to-end communications architecture for cloud radio access networks as well as a detailed comparison to prior approaches, both via theoretical bounds and numerical simulations. Recent work has that the following high-level approach has numerous advantages: each basestation quantizes its observed signal and sends it to the central processing unit for decoding, which in turn generates signals for the basestations to transmit, and sends them quantized versions. This thesis follows an integer-forcing approach that uses the fact that, if codewords are drawn from a linear codebook, then their integer-linear combinations are themselves codewords. Overall, this architecture requires integer-forcing channel coding from the users to the central processing unit and back, which handles interference between the users’ codewords, as well as integer-forcing source coding from the basestations to the central processing unit and back, which handles correlations between the basestations’ analog signals. Prior work on integer-forcing has proposed and analyzed channel coding strategies as well as a source coding strategy for the basestations to the central processing unit, and this thesis proposes a source coding strategy for the other direction. Iterative algorithms are developed to optimize the parameters of the proposed architecture, which involve real-valued beamforming and equalization matrices and integer-valued coefficient matrices in a quadratic objective. Beyond the cloud radio setting, it is argued that the integer-forcing approach is a promising framework for interference alignment between multiple transmitter-receiver pairs. In this scenario, the goal is to align the interfering data streams so that, from the perspective of each receiver, there seems to be only a signal receiver. Integer-forcing interference alignment accomplishes this objective by having each receiver recover two linear combinations that can then be solved for the desired signal and the sum of the interference. Finally, this thesis investigates the impact of channel coherence on the integer-forcing strategy via numerical simulations

Degrees of Freedom of the 3-User Rank-Deficient MIMO Interference Channel

We provide the degrees of freedom (DoF) characterization for the $3$-user $M_T\times M_R$ multiple-input multiple-output (MIMO) interference channel (IC) with \emph{rank-deficient} channel matrices, where each transmitter is equipped with $M_T$ antennas and each receiver with $M_R$ antennas, and the interfering channel matrices from each transmitter to the other two receivers are of ranks $D_1$ and $D_2$, respectively. One important intermediate step for both the converse and achievability arguments is to convert the fully-connected rank-deficient channel into an equivalent partially-connected full-rank MIMO-IC by invertible linear transformations. As such, existing techniques developed for full-rank MIMO-IC can be incorporated to derive the DoF outer and inner bounds for the rank-deficient case. Our result shows that when the interfering links are weak in terms of the channel ranks, i.e., $D_1+D_2\leq \min(M_T, M_R)$, zero forcing is sufficient to achieve the optimal DoF. On the other hand, when $D_1+D_2> \min(M_T, M_R)$, a combination of zero forcing and interference alignment is in general required for DoF optimality. The DoF characterization obtained in this paper unifies several existing results in the literature.Comment: 28 pages, 7 figures. To appear in IEEE transactions on wireless communication

Computation Alignment: Capacity Approximation without Noise Accumulation

Consider several source nodes communicating across a wireless network to a destination node with the help of several layers of relay nodes. Recent work by Avestimehr et al. has approximated the capacity of this network up to an additive gap. The communication scheme achieving this capacity approximation is based on compress-and-forward, resulting in noise accumulation as the messages traverse the network. As a consequence, the approximation gap increases linearly with the network depth. This paper develops a computation alignment strategy that can approach the capacity of a class of layered, time-varying wireless relay networks up to an approximation gap that is independent of the network depth. This strategy is based on the compute-and-forward framework, which enables relays to decode deterministic functions of the transmitted messages. Alone, compute-and-forward is insufficient to approach the capacity as it incurs a penalty for approximating the wireless channel with complex-valued coefficients by a channel with integer coefficients. Here, this penalty is circumvented by carefully matching channel realizations across time slots to create integer-valued effective channels that are well-suited to compute-and-forward. Unlike prior constant gap results, the approximation gap obtained in this paper also depends closely on the fading statistics, which are assumed to be i.i.d. Rayleigh.Comment: 36 pages, to appear in IEEE Transactions on Information Theor