Sphere Packings, Lattices and Groups

Interference is usually viewed as an obstacle to communication in wireless networks. This paper proposes a new strategy, compute-and-forward, that exploits interference to obtain significantly higher rates between users in a network. The key idea is that relays should decode linear functions of transmitted messages according to their observed channel coefficients rather than ignoring the interference as noise. After decoding these linear equations, the relays simply send them towards the destinations, which given enough equations, can recover their desired messages. The underlying codes are based on nested lattices whose algebraic structure ensures that integer combinations of codewords can be decoded reliably. Encoders map messages from a finite field to a lattice and decoders recover equations of lattice points which are then mapped back to equations over the finite field. This scheme is applicable even if the transmitters lack channel state information.

Compute-and-Forward: Harnessing Interference Through Structured Codes

We explore the feasibility of interference alignment in signal vector space-based only on beamforming-for K-user MIMO interference channels. Our main contribution is to relate the feasibility issue to the problem of determining the solvability of a multivariate polynomial system which is considered extensively in algebraic geometry. It is well known, e.g., from Bezout's theorem, that generic polynomial systems are solvable if and only if the number of equations does not exceed the number of variables. Following this intuition, we classify signal space interference alignment problems as either proper or improper based on the number of equations and variables. Rigorous connections between feasible and proper systems are made through Bernshtein's theorem for the case where each transmitter uses only one beamforming vector. The multibeam case introduces dependencies among the coefficients of a polynomial system so that the system is no longer generic in the sense required by both theorems. In this case, we show that the connection between feasible and proper systems can be further strengthened (since the equivalency between feasible and proper systems does not always hold) by including standard information theoretic outer bounds in the feasibility analysis.

On Feasibility of Interference Alignment in MIMO Interference Networks

Interference alignment is a radical idea that has recently emerged out of the capacity analysis of interference networks. In a relatively short time, this concept has challenged much of the conventional wisdom about the throughput limits of both wired and wireless networks. The technique is based on the idea that if interference or undesired signals are collectively engineered to occupy as low a dimensional space as possible, the desired signals can be more efficiently conveyed and recovered. Interference Alignment: A New Look at Signal Dimensions in a Communication Network introduces the concept via a series of simple linear algebraic examples that very effectively convey the central idea of interference alignment. The ideas behind the various communication theoretic instantiations and applications of the technique are illustrated through simple examples that come across as neat little puzzles which enables the reader to quickly understand the topic. Interference Alignment: A New Look at Signal Dimensions in a Communication Network provides both a tutorial and a survey of the state-of-art on the topic. The numerous concretely stated open problems sprinkled throughout tee up issues for further research for the reader. The presentation style of this tutorial is informal, favoring broad intuition over mathematical rigor and is written to be accessible to graduate students, researchers and professionals working in communication, signal processing, networking or information theory.

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Interference Alignment: A New Look at Signal Dimensions in a Communication Network

We explore the degrees of freedom of M times N user wireless X networks, i.e., networks of M transmitters and N receivers where every transmitter has an independent message for every receiver. We derive a general outer bound on the degrees of freedom region of these networks. When all nodes have a single antenna and all channel coefficients vary in time or frequency, we show that the total number of degrees of freedom of the X network is equal to [(MN)/(M+N-1)] per orthogonal time and frequency dimension. Achievability is proved by constructing interference alignment schemes for X networks that can come arbitrarily close to the outer bound on degrees of freedom. For the case where either M=2 or N=2 we find that the degrees of freedom characterization also provides a capacity approximation that is accurate to within O(1) . For these cases the degrees of freedom outer bound is exactly achievable.

/pdf/interference-alignment-and-the-degrees-of-freedom-of-2zxtdohd4u.pdf

Interference Alignment and the Degrees of Freedom of Wireless $X$ Networks

The paper studies a class of three user Gaussian interference channels. A new layered lattice coding scheme is introduced as a transmission strategy. The use of lattice codes allows for an ldquoalignmentrdquo of the interference observed at each receiver. The layered lattice coding is shown to achieve more than one degree of freedom for a class of interference channels and also achieves rates which are better than the rates obtained using the Han-Kobayashi coding scheme.

A layered lattice coding scheme for a class of three user Gaussian interference channels

Systems, methods, and devices for wireless communication In one aspect an apparatus for wirelessly communicating with a wireless station is provided The apparatus comprises a first transceiver configured to receive a backoff signal from the wireless station during a first time period, the backoff signal configured to indicate a second time period The apparatus further comprises a processor operationally coupled to the first transceiver and configured to refrain the first transceiver from transmitting a wireless signal during the second time period

Systems and methods for low power wake up signal and operations for wlan

This paper studies a symmetric K user Gaussian interference channel with K transmitters and K receivers. A "very strong" interference regime is derived for this channel setup. A "very strong" interference regime is one where the capacity region of the interference channel is the same as the capacity region of the channel with no interference. In this regime, the interference can be perfectly canceled by all the receivers without incurring any rate penalties. A "very strong" interference condition for an example symmetric K user deterministic interference channel is also presented.

Capacity of Symmetric K-User Gaussian Very Strong Interference Channels

Methods and stations for wireless communication are described herein. In some aspects, the station may include a processing circuit configured to process a first signal transmitted to the station, the first signal indicating a target wake up time when an activation signal is expected to be received. The station may further include a wake-up circuit configured to transition a first receiver to an awake state based on the indicated target wake up time. The first receiver is configured to receive the activation signal at the indicated target wake up time. The station may further include a second receiver configured to transition to an awake state based on the first receiver receiving the activation signal and receive a second signal while in the awake state.

Amin Jafarian

Papers

A layered lattice coding scheme for a class of three user Gaussian interference channels

Systems and methods for low power wake up signal and operations for wlan

Capacity of Symmetric K-User Gaussian Very Strong Interference Channels

Method and apparatus using an ultra low power signal with scheduled power save modes

Capacity of Symmetric K-User Gaussian Very Strong Interference Channels