Approximate Sum-Capacity of K-user Cognitive Interference Channels with Cumulative Message Sharing

This paper considers the K user cognitive interference channel with one primary and K-1 secondary/cognitive transmitters with a cumulative message sharing structure, i.e cognitive transmitter $i\in [2:K]$ knows non-causally all messages of the users with index less than i. We propose a computable outer bound valid for any memoryless channel. We first evaluate the sum-rate outer bound for the high- SNR linear deterministic approximation of the Gaussian noise channel. This is shown to be capacity for the 3-user channel with arbitrary channel gains and the sum-capacity for the symmetric K-user channel. Interestingly. for the K user channel having only the K th cognitive know all the other messages is sufficient to achieve capacity i.e cognition at transmitter 2 to K-1 is not needed. Next the sum capacity of the symmetric Gaussian noise channel is characterized to within a constant additive and multiplicative gap. The proposed achievable scheme for the additive gap is based on Dirty paper coding and can be thought of as a MIMO-broadcast scheme where only one encoding order is possible due to the message sharing structure. As opposed to other multiuser interference channel models, a single scheme suffices for both the weak and strong interference regimes. With this scheme the generalized degrees of freedom (gDOF) is shown to be a function of K, in contrast to the non cognitive case and the broadcast channel case. Interestingly, it is show that as the number of users grows to infinity the gDoF of the K-user cognitive interference channel with cumulative message sharing tends to the gDoF of a broadcast channel with a K-antenna transmitter and K single-antenna receivers. The analytical additive additive and multiplicative gaps are a function of the number of users. Numerical evaluations of inner and outer bounds show that the actual gap is less than the analytical one.Comment: Journa

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

Capacity Approximations of Mimo Interference Channels: Beyond Degrees of Freedom

Spectrum sharing allows the coexistence of heterogeneous wireless networks on the same frequency band. Managing the interference between such networks is critically important to ensure high spectrum efficiency, thus motivating the study of multiple-input-multiple-output (MIMO) interference channels (IC) in information theory. This dissertation studies three classes of such interference channels, namely, the MIMO one-to-three IC, the MIMO IC-ZIC, and the MIMO MAC-IC-MAC.The MIMO one-to-three IC is a partially connected three-user IC with multiple antenna terminals, where one transmitter that causes interference is heard at all three receivers, whereas the other two transmitters are heard only by their intended receivers. We present inner and outer bounds on the capacity region of the MIMO one-to-three IC, quantify the gap between the two bounds, and show that the gap is independent of the channel signal-to-noise ratios (SNRs) and interference-to-noise ratios (INRs). In particular, the achievable scheme at the interfering transmitter involves three-level superposition coding with linear precoding based on the generalized singular value decomposition (GSVD) whereas the non-interfering transmitters perform single-user coding with Gaussian codebooks and scaled identity covariances. The outer bound is obtained using genie-aided arguments with various combinations of genie information provided to the receivers. The generalized degrees of freedom (GDoF) region, which can be seen as a high SNR approximation of the capacity region, of the MIMO one-to-three IC is then fully characterized. We study the achievability of the GDoF region and the sum GDoF curve using an analysis tool developed in this dissertation, which we refer to as multidimensional signal-level partitioning. This tool is tailored for demonstrating the achievability of GDoF-tuples of a MIMO network that can be achieved via multi-level superposition coding.The MIMO IC-ZIC is also a partially connected three-user IC consisting of three transmitter-receiver pairs. In the IC-ZIC, the first and second pairs form a two-user IC, the first and third pairs form a one-sided or Z interference channel (ZIC) and the second and third transmitter-receiver pairs taken by themselves are two non-interfering point-to-point links. In this thesis, an explicit inner bound is obtained via a coding scheme is proposed in which the first transmitter employs three-level superposition coding (as in the MIMO one-to-three IC), the second one employs the previously proposed and well-known Karmakar-Varanasi coding scheme (which achieves a constant-gap-to-capacity region of the two-user MIMO IC), and the third transmitter employs single-user coding with a Gaussian codebook (with scaled identity covariance). An explicit single region outer bound based on genie-aided arguments is then obtained. The gap between the inner and outer bounds is then shown to be within a quantifiable gap to the capacity region and the gap is independent of channel SNRs and INRs. The GDoF region is then characterized and analyzed in a variety of channel settings. The difficulty in this part of the research lies in the quantification of the gap between the 28-inequality inner bound and the 33-inequality outer bound, which is characterized via a series of supporting lemmas that reveal the relationship between the entropy terms in the inner and outer bounds.The MIMO MAC-IC-MAC consists of two interfering MACs in which there is interference only from one transmitter of each MAC to the receiver of the other MAC. Two achievable rate regions that are within a quantifiable gap of the capacity region for the discrete-memoryless semi-deterministic MAC-IC-MAC were obtained in a previous published work by Pang and Varanasi using inner and outer bounds that are unions of polytopes. In the dissertation, we obtain single region inner and outer bounds that characterize a constant-gap-to-capacity region of the MIMO MAC-IC-

A digital interface for Gaussian relay and interference networks: Lifting codes from the discrete superposition model

For every Gaussian network, there exists a corresponding deterministic network called the discrete superposition network. We show that this discrete superposition network provides a near-optimal digital interface for operating a class consisting of many Gaussian networks in the sense that any code for the discrete superposition network can be naturally lifted to a corresponding code for the Gaussian network, while achieving a rate that is no more than a constant number of bits lesser than the rate it achieves for the discrete superposition network. This constant depends only on the number of nodes in the network and not on the channel gains or SNR. Moreover the capacities of the two networks are within a constant of each other, again independent of channel gains and SNR. We show that the class of Gaussian networks for which this interface property holds includes relay networks with a single source-destination pair, interference networks, multicast networks, and the counterparts of these networks with multiple transmit and receive antennas. The code for the Gaussian relay network can be obtained from any code for the discrete superposition network simply by pruning it. This lifting scheme establishes that the superposition model can indeed potentially serve as a strong surrogate for designing codes for Gaussian relay networks. We present similar results for the K x K Gaussian interference network, MIMO Gaussian interference networks, MIMO Gaussian relay networks, and multicast networks, with the constant gap depending additionally on the number of antennas in case of MIMO networks.Comment: Final versio