Anas Chaaban

Free-Space Optical Communications: Capacity Bounds, Approximations, and a New Sphere-Packing Perspective

The capacity of the free-space optical channel is studied. A new recursive approach for bounding the capacity of the channel based on sphere-packing is proposed. This approach leads to new capacity upper bounds for a channel with a peak intensity constraint or an average intensity constraint. Under an average constraint only, the derived bound is tighter than an existing sphere-packing bound derived earlier by Farid and Hranilovic. The achievable rate of a truncated-Gaussian input distribution is also derived. It is shown that under both average and peak constraints, this achievable rate and the sphere-packing bounds are within a small gap at high SNR, leading to a simple high-SNR capacity approximation. Simple fitting functions that capture the best known achievable rate for the channel are provided. These functions can be of practical importance especially for the study of systems operating under atmospheric turbulence and misalignment conditions.

The degrees of freedom of the MIMO Y-channel

The degrees of freedom (DoF) of the MIMO Y-channel, a multi-way communication network consisting of 3 users and a relay, are characterized for arbitrary number of antennas. The converse is provided by cut-set bounds and novel genie-aided bounds. The achievability is shown by a scheme that uses beamforming to establish network coding on-the-fly at the relay in the uplink, and zero-forcing pre-coding in the downlink. It is shown that the network has min{2M2+2M3, M1+ M2 + M3,2N} DoF, where Mj and N represent the number of antennas at user j and the relay, respectively. Thus, in the extreme case where M1+M2+M3 dominates the DoF expression and is smaller than N, the network has the same DoF as the MAC between the 3 users and the relay. In this case, a decode and forward strategy is optimal. In the other extreme where 2N dominates, the DoF of the network is twice that of the aforementioned MAC, and hence network coding is necessary. As a byproduct of this work, it is shown that channel output feedback from the relay to the users has no impact on the DoF of this channel.

On the Generalized Degrees of Freedom of the Gaussian Interference Relay Channel

The symmetric two-user Gaussian interference relay channel (IRC) is studied from a generalized degrees of freedom (GDoF) perspective. While it is known that the relay does not in crease the DoF of the IRC, such a characterization has not been reported for the GDoF yet. The focus of this paper is on all cases where the interference link is stronger than the link from the source to the relay. This regime basically covers half the space of all possible parameters of the IRC. By using genie-aided approaches, new sum-capacity upper bounds are derived. These bounds are then compared with rates achieved with a novel transmission scheme, which is based on a functional decode-and-forward (FDF) strategy. It is shown that the GDoF of the IRC is achieved by FDF in the given regime, and that a relay can indeed increase the GDoF of IRC. Finally, the FDF scheme is compared with other schemes like decode-and-forward as well as compress-and-forward at low, moderate, and high signal-to-noise ratios.

Approximate Sum-Capacity of the Y-Channel

A network where three users want to establish multiple unicasts between each other via a relay is considered. This network is called the Y-channel and resembles an elemental ingredient of future wireless networks. The sum-capacity of this network is studied. A characterization of the sum-capacity within an additive gap of 2 bits, and a multiplicative gap of 4, for all values of channel gains and transmit powers is obtained. Contrary to similar setups where the cut-set bounds can be achieved within a constant gap, they cannot be achieved in our case, where they are dominated by our new genie-aided bounds. Furthermore, it is shown that a time-sharing strategy, in which at each time two users exchange information using coding strategies of the bidirectional relay channel, achieves the upper bounds to within a constant gap. This result is further extended to the K-user case, where it is shown that the same scheme achieves the sum-capacity within 2log(K-1) bits.

The capacity region of the linear shift deterministic Y-channel

The linear shift deterministic Y-channel is studied. That is, we have three users and one relay, where each user wishes to broadcast one message to each other user via the relay, resulting in a multi-way relaying setup. The cut-set bounds for this setup are shown to be not sufficient to characterize its capacity region. New upper bounds are derived, which when combined with the cut-set bounds provide an outer bound on the capacity region. It is shown that this outer bound is achievable, and as a result, the capacity region of the linear shift deterministic Y-channel is characterized.

Multi-way Communications: An Information Theoretic Perspective

Multi-way communication is a means to significantly improve the spectralefficiency of wireless networks. For instance, in a bi-directional ortwo-way communication channel, two users can simultaneously usethe transmission medium to exchange information, thus achieving upto twice the rate that would be achieved had each user transmittedseparately. Multi-way communications provides an overview on the developmentsin this research area since it has been initiated by Shannon.The basic two-way communication channel is considered first, followedby the two-way relay channel obtained by the deployment of an additionalcooperative relay node to improve the overall communicationperformance. This basic setup is then extended to multi-user systems.For all these setups, fundamental limits on the achievable rates are reviewed,thereby making use of a linear high-SNR deterministic channelmodel to provide valuable insights which are helpful when discussingthe coding schemes for Gaussian channel models in detail. Several toolsand communication strategies are used in the process, including butnot limited to computation, signal-space alignment, and nested-latticecodes. Finally, extensions of multi-way communication channels to multipleantenna settings are discussed.

Fundamental Limits of Parallel Optical Wireless Channels: Capacity Results and Outage Formulation

Multi-channel (MC) optical wireless communication (OWC) systems employing wave-division multiplexing for outdoors free-space optical communications, or multi-user time-division multiple access for indoors visible-light communications, e.g., can be modeled as parallel channels. Multi-input multi-output OWC systems can also be transformed, possibly with some performance loss, to parallel channels using pre-/post-coding. Studying the performance of such MC-OWC systems requires characterizing the capacity of the underlying parallel channels. In this paper, upper and lower bounds on the capacity of constant parallel OWC channels with a total average intensity constraint are derived. Then, this paper focuses on finding intensity allocations that maximize the lower bounds given channel-state information at the transmitter (CSIT). Due to its nonconvexity, the Karush–Kuhn–Tucker conditions are used to describe a list of candidate allocations. Instead searching exhaustively for the best solution, low-complexity near-optimal algorithms are proposed. The resulting optimized lower bound nearly coincides with capacity at high signal-to-noise ratio (SNR). Under a quasi-static channel model and in the absence of CSIT, outage probability upper and lower bounds are derived. Those bounds also meet at high SNR, thus characterizing the outage capacity in this regime. Finally, the results are extended to a system with both average and peak intensity constraints.

(Sub-)Optimality of Treating Interference as Noise in the Cellular Uplink With Weak Interference

Despite the simplicity of the scheme of treating interference as noise (TIN), it was shown to be sum-capacity optimal in the Gaussian interference channel (IC) with very-weak (noisy) interference. In this paper, the two-user IC is altered by introducing an additional transmitter that wants to communicate with one of the receivers of the IC. The resulting network thus consists of a point-to-point channel interfering with a multiple access channel (MAC) and is denoted by PIMAC. The sum-capacity of the PIMAC is studied with main focus on the optimality of TIN. It turns out that TIN in its naive variant, where all transmitters are active and both receivers use TIN for decoding, is not the best choice for the PIMAC. In fact, a scheme that combines both time division multiple access and TIN (TDMA–TIN) strictly outperforms the naive-TIN scheme. Furthermore, it is shown that in some regimes, TDMA–TIN achieves the sum-capacity for the deterministic PIMAC and the sum-capacity within a constant gap for the Gaussian PIMAC. In addition, it is shown that, even for very-weak interference, there are some regimes where a combination of interference alignment with power control and TIN at the receiver side outperforms TDMA–TIN. As a consequence, on the one hand, TIN in a cellular uplink is approximately optimal in certain regimes. On the other hand, those regimes cannot be simply described by the strength of interference.

The capacity region of the 3-user Gaussian interference channel with mixed strong-very strong interference

We consider the 3-user Gaussian interference channel and provide an outer bound on its capacity region. Under some conditions, which we call the mixed strong-very strong interference conditions, this outer bound is achievable. These conditions correspond to the case where at each receiver, one transmitter is causing strong interference and the other is causing very strong interference. Therefore, we characterize the capacity region of the 3-user interference channel with mixed strong-very strong interference.

The Approximate Capacity Region of the Gaussian Y-Channel via the Deterministic Approach

A full-duplex wireless network with three users that want to establish full message exchange via a relay is considered. Thus, this network which is known as the Y-channel has a total of six messages, two outgoing, and two incoming at each user. The users are not physically connected, and thus the relay is essential for their communication. The deterministic Y-channel is considered first, its capacity region is characterized, and shown not to be given by the cut-set bounds. The capacity achieving scheme has three different components (strategies): 1) a bidirectional; 2) a cyclic; and 3) a unidirectional strategy. Network coding is used to realize the bidirectional and the cyclic strategies, and thus to prove the achievability of the capacity region. The result is then extended to the Gaussian Y-channel where the capacity region is characterized within a constant gap independent of the channel parameters.