Abolfazl S. Motahari

Capacity Bounds for the Gaussian Interference Channel

The capacity region of the two-user Gaussian interference channel (IC) is studied. Three classes of channels are considered: weak, one-sided, and mixed Gaussian ICs. For the weak Gaussian IC, a new outer bound on the capacity region is obtained that outperforms previously known outer bounds. The sum capacity for a certain range of channel parameters is derived. For this range, it is proved that using Gaussian codebooks and treating interference as noise are optimal. It is shown that when Gaussian codebooks are used, the full Han-Kobayashi achievable rate region can be obtained by using the naive Han-Kobayashi achievable scheme over three frequency bands (equivalently, three subspaces). For the one-sided Gaussian IC, an alternative proof for the Satos outer bound is presented. We derive the full Han-Kobayashi achievable rate region when Gaussian codebooks are utilized. For the mixed Gaussian IC, a new outer bound is obtained that outperforms previously known outer bounds. For this case, the sum capacity for the entire range of channel parameters is derived. It is proved that the full Han-Kobayashi achievable rate region using Gaussian codebooks is equivalent to that of the one-sided Gaussian IC for a particular range of channel parameters.

Real Interference Alignment: Exploiting the Potential of Single Antenna Systems

In this paper, we develop the machinery of real interference alignment. This machinery is extremely powerful in achieving the sum degrees of freedom (DoF) of single antenna systems. The scheme of real interference alignment is based on designing single-layer and multilayer constellations used for modulating information messages at the transmitters. We show that constellations can be aligned in a similar fashion as that of vectors in multiple antenna systems and space can be broken up into fractional dimensions. The performance analysis of the signaling scheme makes use of a recent result in the field of Diophantine approximation, which states that the convergence part of the Khintchine-Groshev theorem holds for points on nondegenerate manifolds. Using real interference alignment, we obtain the sum DoF of two model channels, namely the Gaussian interference channel (IC) and the X channel. It is proved that the sum DoF of the K-user IC is (K/2) for almost all channel parameters. We also prove that the sum DoF of the X-channel with K transmitters and M receivers is (K M/K + M - 1) for almost all channel parameters.

Signaling over MIMO Multi-Base Systems: Combination of Multi-Access and Broadcast Schemes

A new structure for multi-base systems is studied in which each user receives data from two nearby base stations, rather than only from the strongest one. This system can be considered as a combination of broadcast and multi-access channels. By taking advantages of both perspectives, an achievable rate region for a discrete memoryless channel modeled by Pr(y1,y2|x1,x2 ) is derived. In this model, x1 and x2 represent the transmitted signals by the transmitter one and two, respectively, and y1 and y2 denote the received signals by the receiver one and two, respectively. In this derivation, it is assumed that each transmitter is unaware of the data of the other transmitter, and therefore x1 and x2 are independent. To investigate the advantage of this scheme, an efficient signaling method which works at a corner point of the achievable region for multiple-antenna scenarios is developed. In the proposed scheme, each base station only requires the state information of the channels between the other base station and each user. In this paper, the signaling scheme is elaborated for the case that each transmitter/receiver is equipped with three antennas. It is proven that in such a scenario, the multiplexing gain of four is achievable, which outperforms any other conventional schemes

Capacity bounds for the Gaussian Interference Channel

The capacity region of the two-user Gaussian interference channel (IC) is studied. Two classes of channels are considered: weak and mixed Gaussian IC. For the weak Gaussian IC, a new outer bound on the capacity region is obtained that outperforms previously known outer bounds. The sum capacity for a certain range of channel parameters is derived. For this range, it is proved that using Gaussian codebooks and treating interference as noise is optimal. It is shown that when Gaussian codebooks are used, the full Han-Kobayashi (HK) achievable rate region can be obtained by using the naive HK achievable scheme over three frequency bands. For the mixed Gaussian IC, a new outer bound is obtained that outperforms previously known outer bounds. For this case, the sum capacity for the entire range of channel parameters is derived. It is proved that the full HK achievable rate region using Gaussian codebooks is equivalent to that of the one-sided Gaussian IC for a particular range of channel parameters.

Interference alignment for the K user MIMO interference channel

We consider the K user Multiple Input Multiple Output (MIMO) Gaussian interference channel with M antennas at each transmitter and N antennas at each receiver. It is assumed that channel coefficients are fixed and are available at all transmitters and at all receivers. The main objective of this paper is to characterize the total Degrees Of Freedom (DOF) for this channel. Using a new interference alignment technique which has been recently introduced in [1], we show that MN over M+N K degrees of freedom can be achieved for almost all channel realizations. Also, a new upper-bound on the total DOF for this channel is derived. This upper-bound coincides with our achievable DOF for K ≥ Ku ≜ M+N over gcd(M,N) where gcd(M,N) denotes the greatest common divisor of M and N. This gives an exact characterization of DOF for MIMO Gaussian interference channel in the case of K ≥ Ku.

On the degrees of freedom of MIMO X channel with delayed CSIT

The multiple-input multiple-output (MIMO) Gaussian X channel in i.i.d. fading environment and with delayed channel state information at transmitters (delayed CSIT) is considered. It is assumed that each transmitter has M antennas and each receiver has N antennas. New achievable results on the sum degrees of freedom (DoF) of this channel are provided and shown to be tight for all possible values of M and N except for 1/2 <; N/M <; 4/3. It is noteworthy that for certain values of M and N, the channel DoF coincides with the DoF of the broadcast channel obtained by assuming perfect transmitter cooperation.

On the capacity of the half-duplex diamond channel

The diamond channel is a dual-hop communication system composed of a source, and a destination connected through two noninterfering relays. Operating in the half-duplex mode, relays are not capable of simultaneous transmission and reception of signals. This paper studies coding and scheduling schemes achieving within constant gap from the maximum achievable rate possible assuming the scheduling is fixed for all messages and known to all nodes prior to transmission. It is shown that under constant power constraints, a simple transmission scheme for relays is within 0.71 bits of the optimum rate. It is also demonstrated that the proposed scheme can attain the optimum rate, when channels satisfy a certain property. Furthermore, it is proved that under average power constraints, the same scheme can be used to achieve within 3.6 bits of the optimum rate.

Information Theory of DNA Shotgun Sequencing

DNA sequencing is the basic workhorse of modern day biology and medicine. Shotgun sequencing is the dominant technique used: many randomly located short fragments called reads are extracted from the DNA sequence, and these reads are assembled to reconstruct the original sequence. A basic question is: given a sequencing technology and the statistics of the DNA sequence, what is the minimum number of reads required for reliable reconstruction? This number provides a fundamental limit to the performance of any assembly algorithm. For a simple statistical model of the DNA sequence and the read process, we show that the answer admits a critical phenomenon in the asymptotic limit of long DNA sequences: if the read length is below a threshold, reconstruction is impossible no matter how many reads are observed, and if the read length is above the threshold, having enough reads to cover the DNA sequence is sufficient to reconstruct. The threshold is computed in terms of the Renyi entropy rate of the DNA sequence. We also study the impact of noise in the read process on the performance.

Secure broadcasting : The secrecy rate region

In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with confidential messages. We present an inner bound on the secrecy capacity region for this model. The inner bound coding scheme is based on a combination of random binning and the Gelfand-Pinsker bining. This scheme matches the Martons inner bound on the broadcast channel without confidentiality constraint. We further study the situation where the channels are degraded. For the degraded broadcast channel with confidential messages, we present the secrecy capacity region. Our achievable coding scheme is based on Covers superposition scheme and random binning. We refer to this scheme as secret superposition scheme. In this scheme, we show that randomization in the first layer increases the secrecy rate of the second layer. This capacity region matches the capacity region of the degraded broadcast channel without security constraint. It also matches the secrecy capacity for the conventional wire-tap channel. Our converse proof is based on a combination of the converse proof of the conventional degraded broadcast channel and Csiszar lemma.

Secrecy capacity region of Gaussian broadcast channel

In this paper, we first consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-taper also receives the transmitted signal. We assume that the signals are transmitted over additive white Gaussian noise channels. We characterize the secrecy capacity region of this channel. Our achievable coding scheme is based on superposition coding and the random binning. We refer to this scheme as Secret Superposition Coding. The converse proof combines the converse proof for the conventional Gaussian broadcast channel and the perfect secrecy constraint. This capacity region matches the capacity region of the broadcast channel without security constraint. It also matches the secrecy capacity of the wire-tap channel. Based on the rate characterization of the secure Gaussian broadcast channel, we then use a multilevel coding approach for the slowly fading wire-tap. We assume that the transmitter only knows the eavesdroppers channel. In this approach, source node sends secure layered coding and the receiver viewed as a continuum ordered users. We derive optimum power allocation for the layers which maximizes the total average rate.