This thesis looks at the problem of designing a coding strategy for interference channels with rate-limited transmitter cooperation. We first consider a simple communication model in which the classic two-user Gaussian interference channel is augmented by rate-limited conferencing links between the transmitters. The main contribution is a partial zero-forcing precoding strategy based on a shared-private rate splitting scheme at the transmitter, in which each transmitter communicates part of its message to the other transmitter, and subsequently partially pre-subtracts the interfering signal using a zero-forcing precoder. We extend the proposed strategy to a class of multiuser interference channels, and outline a distributed algorithm to compute the precoder coefficients. The partial zero-forcing precoding strategy is shown to be particularly effective in certain high SNR/INR regimes, and simulation results for a multicell system highlight the cooperation gain due to the proposed strategy.

This thesis looks at the problem of designing a coding strategy for interference channels with rate-limited transmitter cooperation. We first consider a simple communication model in which the classic two-user Gaussian interference channel is augmented by rate-limited conferencing links between the transmitters. The main contribution is a partial zero-forcing precoding strategy based on a shared-private rate splitting scheme at the transmitter, in which each transmitter communicates part of its message to the other transmitter, and subsequently partially pre-subtracts the interfering signal using a zero-forcing precoder. We extend the proposed strategy to a class of multiuser interference channels, and outline a distributed algorithm to compute the precoder coefficients. The partial zero-forcing precoding strategy is shown to be particularly effective in certain high SNR/INR regimes, and simulation results for a multicell system highlight the cooperation gain due to the proposed strategy.

Today and future wireless networks are facing one of their greatest limiting factors:interference. This is due to the unprecedented increase in the number of connecteddevices. Therefore, in order to meet the ever increasing demand for data rate andquality of services, more advanced techniques than what we have today are requiredto deal with interference. This thesis takes a step towards interference managementin multiuser wireless systems by means of relaying and cooperation. We study fourfundamental building blocks in network information theory, propose new codingschemes, and derive limits on the capacity regions. The first problem we consider is the one-sided interference channel with bidirectional and rate-limited receiver cooperation. We propose a coding scheme that tailors two versions of superposition coding with classical relaying protocols. Theproposed scheme unifies and recovers previous results for the unidirectional coop-eration, yet in simpler forms. Analytical and numerical results confirm the benefitsof cooperation and illuminate the ideas behind the coding strategy. The second problem generalizes the first one by allowing the existence of bothcrossover links in the channel. We propose a coding scheme for this channel byextending noisy network coding to encompass rate-splitting at the encoders. Theachievable rate region is shown to be the same as a region achieved by explicitbinning. As a corollary, we prove that noisy network coding achieves the capacityregion of the Gaussian channel within 1 bit, under strong interference. Our resultis among the first to show constant-gap optimality of noisy network coding for amultiple-unicast problem, and to demonstrate equivalence in terms of achievablerates of two different coding approaches for a noisy interference network. We follow up by introducing a dedicated relay into the interference channelwhich simultaneously helps both receivers. For this third problem, the interferencechannel with a relay, we propose new coding schemes based on layered codes for long- and short-message quantize-forward techniques. The short-message schemesshow improvements in the achievable rates compared to other known coding tech-niques, especially when the channel is asymmetric, while relaxing the excessive delayissue of the long-message scheme. The analysis also reveals the trade-off betweenachievable rates, encoding and decoding delays, and complexity. In the fourth problem, we propose a new model for cooperative communication,the interfering relay channels, which consists of two neighboring relay channelsinducing interference to each other. Each relay, by utilizing a finite-capacity andnoise-free link to its own receiver, helps the receiver decode the desired message.We characterize the exact and approximate capacity region and sum-capacity forvarious classes of channels. The established results generalize and unify severalknown results for the relay and interference channels.The methods and results shown in this thesis aim at providing insight intopotential techniques for cooperative interference management in real-world systems. / <p>QC 20131001</p>

Sharing communication resources in wireless communication networks, due to the ever increasing growth in the number of users and the growing demand for higher data rates, appears to be inevitable. Consequently, present wireless communication networks should provide service for a large number of users through a frequency selective and interference limited medium rather than a single band, noise limited channel. In this thesis, we study a Gaussian interference network with orthogonal frequency sub-bands with slow faded and frequency-selective channel coefficients. The network is decentralized in the sense that there is no central node to assign the frequency sub-bands to the users. Moreover, due to lack of a feedback link between the two ends of any transmitter-receiver pair, all transmitters are unaware of the channel coefficients. Since the channel is assumed to be static during the communication period of interest, the concept of outage probability is employed in order to assess the performance of the network. In a scenario where all transmitters distribute their available power uniformly across the sub-bands, we investigate the problem of how establishing a nonzero correlation ρ among the Gaussian signals transmitted by each user along different frequency sub-bands can improve the outage probability at each of the receivers. Specifically, we show in a general k-user interference channel over N orthogonal frequency sub-bands that , when receivers treat interference as noise, ρ=0 is a point of local extremum for the achievable rate at each receiver, for any realization of channel coefficients. Moreover, in the case of K=2 with arbitrary number of sub-bands, it is verified that there exists a finite level of Signal-to-Noise Ratio (SNR) such that the achievable rate has a local minimum at ρ=0, which is not necessarily the case when K>2. We then concentrate on a 2-user interference channel over 2 orthogonal frequency sub-bands and characterize the behavior of the outage probability in the high SNR regime. We consider two simple decoding strategies at the receiver. In the first scenario, receivers simply treat interference as noise. In the second scenario, the receivers have the choice either to decode the desired signal treating interference as noise or to decode interference treating the desired signal as noise before decoding the interference free signal. Indeed, in both cases, we first show that the achievable rate is an increasing function of ρ in the high SNR regime, which suggests to repeat the same signal over the sub-bands. This observation, in a sense, reflects to the behavior of the outage probability, the scaling behavior of which in the high SNR regime is characterized for the Rayleigh fading scenario.

We consider a wireless communication system in which there are N transmitter-receiver pairs and each transmitter wants to communicate with its corresponding receiver. This is modelled as an interference channel. We propose power allocation algorithms for increasing the sum rate of two and three user interference channels. The channels experience fast fading and there is an average power constraint on each transmitter. In this case receivers use successive decoding under strong interference, instead of treating interference as noise all the time. Next, we u se game theoretic approach for power allocation where each receiver treats interference as noise. Each transmitter-receiver pair aims to maximize its long-term average transmission rate subject to an average power constraint. We formulate a stochastic game for this system in three different scenarios. First, we assume that each user knows all direct and crosslink channel gains. Next, we assume that each user knows channel gains of only the links that are incident on its receiver. Finally, we assume that each use r knows only its own direct link channel gain. In all cases, we formulate the problem of finding the Nash equilibrium(NE) as a variational in equality problem. For the game with complete channel knowledge, we present an algorithm to solve the VI and we provide weaker sufficient conditions for uniqueness of the NE than the sufficient conditions available in the literature. Later, we present a novel heuristic for solving the VI under general channel conditions. We also provide a distributed algorithm to compute Pare to optimal solutions for the proposed games. We use Bayesian learning that guarantees convergence to an Ɛ-Nash equilibrium for the incomplete information game with direct link channel gain knowledge only, that does not require knowledge of the power policies of other users but requires feedback of the interference power values from a receiver to its corresponding transmitter. Later, we consider a more practical scenario in which each transmitter transmits data at a certain rate using a power that depends on the channel gain to its receiver. If a receiver can successfully receive the message, it sends an acknowledgement(ACK), else it sends a negative ACK(NACK). Each user aims to maximize its probability of successful transmission. We formulate this problem as a stochastic game and propose a fully distributed learning algorithm to find a correlated equilibrium(CE). In addition, we use a no regret algorithm to find a coarse correlated equilibrium(CCE) for our power allocation game. We also propose a fully distributed learning algorithm to find a Pareto optimal solution. In general Pareto points do not guarantee fairness among the users. Therefore we also propose an algorithm to compute a Nash bargaining solution which is Pareto optimal and provides fairness among the users. Finally, we extend these results when each transmitter sends data at multiple rates rather than at a fixed rate.

Channel sharing is known as a unique solution to satisfy the increasing demand for the spectral-efficient communication. In the channel sharing technique, several users concurrently communicate through a shared wireless medium. In such a scheme, the interference of users over each other is the main source of impairment. The task of performance evaluation and signaling design in the presence of such interference is known as a challenging problem. In this thesis, a system including $n$ parallel interfering AWGN transmission paths is considered, where the power of the transmitters are subject to some upper-bounds. For such a system, we obtain a closed form for the boundaries of the rate region based on the Perron-Frobenius eigenvalue of some non-negative matrices. While the boundary of the rate region for the case of unconstrained power is a well-established result, this is the first result for the case of constrained power. This result is utilized to develop an efficient user removal algorithm for congested networks. In these networks, it may not be possible for all users to attain a required Quality of Service (QoS). In this case, the solution is to remove some of the users from the set of active ones. The problem of finding the set of removed users with the minimum cardinality is claimed to be an NP-complete problem. In this thesis, a novel sub-optimal removal algorithm is proposed, which relies on the derived boundary of the rate region in the first part of the thesis. Simulation results show that the proposed algorithm outperforms other known schemes.

Channel sharing is known as a unique solution to satisfy the increasing demand for the spectral-efficient communication. In the channel sharing technique, several users concurrently communicate through a shared wireless medium. In such a scheme, the interference of users over each other is the main source of impairment. The task of performance evaluation and signaling design in the presence of such interference is known as a challenging problem. In this thesis, a system including $n$ parallel interfering AWGN transmission paths is considered, where the power of the transmitters are subject to some upper-bounds. For such a system, we obtain a closed form for the boundaries of the rate region based on the Perron-Frobenius eigenvalue of some non-negative matrices. While the boundary of the rate region for the case of unconstrained power is a well-established result, this is the first result for the case of constrained power. This result is utilized to develop an efficient user removal algorithm for congested networks. In these networks, it may not be possible for all users to attain a required Quality of Service (QoS). In this case, the solution is to remove some of the users from the set of active ones. The problem of finding the set of removed users with the minimum cardinality is claimed to be an NP-complete problem. In this thesis, a novel sub-optimal removal algorithm is proposed, which relies on the derived boundary of the rate region in the first part of the thesis. Simulation results show that the proposed algorithm outperforms other known schemes.

Ad hoc networks and bluetooth systems operating over the unlicensed ISM band are in-stances of decentralized wireless networks. By definition, a decentralized network is com-posed of separate transmitter-receiver pairs where there is no central controller to assign the resources to the users. As such, resource allocation must be performed locally at each node. Users are anonymous to each other, i.e., they are not aware of each other's code-books. This implies that multiuser detection is not possible and users treat each other as noise. Multiuser interference is known to be the main factor that limits the achievable rates in such networks particularly in the high Signal-to-Noise Ratio (SNR) regime. Therefore, all users must follow a distributed signaling scheme such that the destructive effect of interference on each user is minimized, while the resources are fairly shared. In chapter 2 we consider a decentralized wireless communication network with a fixed number of frequency sub-bands to be shared among several transmitter-receiver pairs. It is assumed that the number of active users is a realization of a random variable with a given probability mass function. Moreover, users are unaware of each other's codebooks and hence, no multiuser detection is possible. We propose a randomized Frequency Hopping (FH) scheme in which each transmitter randomly hops over a subset of sub-bands from transmission slot to transmission slot. Assuming all users transmit Gaussian signals, the distribution of the noise plus interference is mixed Gaussian, which makes calculation of the mutual information between the transmitted and received signals of each user intractable. We derive lower and upper bounds on the mutual information of each user and demonstrate that, for large SNR values, the two bounds coincide. This observation enables us to compute the sum multiplexing gain of the system and obtain the optimum hopping strategy for maximizing this quantity. We compare the performance of the FH system with that of the Frequency Division (FD) system in terms of the following performance measures: average sum multiplexing gain and average minimum multiplexing gain per user. We show that (depending on the probability mass function of the number of active users) the FH system can offer a significant improvement in terms of the aforementioned measures. In the sequel, we consider a scenario where the transmitters are unaware of the number of active users in the network as well as the channel gains. Developing a new upper bound on the differential entropy of a mixed Gaussian random vector and using entropy power inequality, we obtain lower bounds on the maximum transmission rate per user to ensure a specified outage probability at a given SNR level. We demonstrate that the so-called outage capacity can be considerably higher in the FH scheme than in the FD scenario for reasonable distributions on the number of active users. This guarantees a higher spectral efficiency in FH compared to FD. Chapter 3 addresses spectral efficiency in decentralized wireless networks of separate transmitter-receiver pairs by generalizing the ideas developed in chapter 2. Motivated by random spreading in Code Division Multiple Access (CDMA), a signaling scheme is introduced where each user's code-book consists of two groups of codewords, referred to as signal codewords and signature codewords. Each signal codeword is a sequence of independent Gaussian random variables and each signature codeword is a sequence of independent random vectors constructed over a globally known alphabet. Using a conditional entropy power inequality and a key upper bound on the differential entropy of a mixed Gaussian random vector, we develop an inner bound on the capacity region of the decentralized network. To guarantee consistency and fairness, each user designs its signature codewords based on maximizing the average (with respect to a globally known distribution on the channel gains) of the achievable rate per user. It is demonstrated how the Sum Multiplexing Gain (SMG) in the network (regardless of the number of users) can be made arbitrarily close to the SMG of a centralized network with an orthogonal scheme such as Time Division (TD). An interesting observation is that in general the elements of the vectors in a signature codeword must not be equiprobable over the underlying alphabet in contrast to the use of binary Pseudo-random Noise (PN) signatures in randomly spread CDMA where the chip elements are +1 or -1 with equal probability. The main reason for this phenomenon is the interplay between two factors appearing in the expression of the achievable rate, i.e., multiplexing gain and the so-called interference entropy factor. In the sequel, invoking an information theoretic extremal inequality, we present an optimality result by showing that in randomized frequency hopping which is the main idea in the prevailing bluetooth devices in decentralized networks, transmission of independent signals in consecutive transmission slots is in general suboptimal regardless of the distribution of the signals. Finally, chapter 4 addresses a decentralized Gaussian interference channel consisting of two block-asynchronous transmitter-receiver pairs. We consider a scenario where the rate of data arrival at the encoders is considerably low and codewords of each user are transmitted at random instants depending on the availability of enough data for transmission. This makes the transmitted signals by each user look like scattered bursts along the time axis. Users are block-asynchronous meaning there exists a delay between their transmitted signal bursts. The proposed model for asynchrony assumes the starting point of an interference burst is uniformly distributed along the transmitted codeword of any user. There is also the possibility that each user does not experience interference on a transmitted codeword at all. Due to the randomness of delay, the channels are non-ergodic in the sense that the transmitters are unaware of the location of interference bursts along their transmitted codewords. In the proposed scheme, upon availability of enough data in its queue, each user follows a locally Randomized Masking (RM) strategy where the transmitter quits transmitting the Gaussian symbols in its codeword independently from symbol interval to symbol interval. An upper bound on the probability of outage per user is developed using entropy power inequality and a key upper bound on the differential entropy of a mixed Gaussian random variable. It is shown that by adopting the RM scheme, the probability of outage is considerably less than the case where both users transmit the Gaussian symbols in their codewords in consecutive symbol intervals, referred to as Continuous Transmission (CT).

Ad hoc networks and bluetooth systems operating over the unlicensed ISM band are in-stances of decentralized wireless networks. By definition, a decentralized network is com-posed of separate transmitter-receiver pairs where there is no central controller to assign the resources to the users. As such, resource allocation must be performed locally at each node. Users are anonymous to each other, i.e., they are not aware of each other's code-books. This implies that multiuser detection is not possible and users treat each other as noise. Multiuser interference is known to be the main factor that limits the achievable rates in such networks particularly in the high Signal-to-Noise Ratio (SNR) regime. Therefore, all users must follow a distributed signaling scheme such that the destructive effect of interference on each user is minimized, while the resources are fairly shared. In chapter 2 we consider a decentralized wireless communication network with a fixed number of frequency sub-bands to be shared among several transmitter-receiver pairs. It is assumed that the number of active users is a realization of a random variable with a given probability mass function. Moreover, users are unaware of each other's codebooks and hence, no multiuser detection is possible. We propose a randomized Frequency Hopping (FH) scheme in which each transmitter randomly hops over a subset of sub-bands from transmission slot to transmission slot. Assuming all users transmit Gaussian signals, the distribution of the noise plus interference is mixed Gaussian, which makes calculation of the mutual information between the transmitted and received signals of each user intractable. We derive lower and upper bounds on the mutual information of each user and demonstrate that, for large SNR values, the two bounds coincide. This observation enables us to compute the sum multiplexing gain of the system and obtain the optimum hopping strategy for maximizing this quantity. We compare the performance of the FH system with that of the Frequency Division (FD) system in terms of the following performance measures: average sum multiplexing gain and average minimum multiplexing gain per user. We show that (depending on the probability mass function of the number of active users) the FH system can offer a significant improvement in terms of the aforementioned measures. In the sequel, we consider a scenario where the transmitters are unaware of the number of active users in the network as well as the channel gains. Developing a new upper bound on the differential entropy of a mixed Gaussian random vector and using entropy power inequality, we obtain lower bounds on the maximum transmission rate per user to ensure a specified outage probability at a given SNR level. We demonstrate that the so-called outage capacity can be considerably higher in the FH scheme than in the FD scenario for reasonable distributions on the number of active users. This guarantees a higher spectral efficiency in FH compared to FD. Chapter 3 addresses spectral efficiency in decentralized wireless networks of separate transmitter-receiver pairs by generalizing the ideas developed in chapter 2. Motivated by random spreading in Code Division Multiple Access (CDMA), a signaling scheme is introduced where each user's code-book consists of two groups of codewords, referred to as signal codewords and signature codewords. Each signal codeword is a sequence of independent Gaussian random variables and each signature codeword is a sequence of independent random vectors constructed over a globally known alphabet. Using a conditional entropy power inequality and a key upper bound on the differential entropy of a mixed Gaussian random vector, we develop an inner bound on the capacity region of the decentralized network. To guarantee consistency and fairness, each user designs its signature codewords based on maximizing the average (with respect to a globally known distribution on the channel gains) of the achievable rate per user. It is demonstrated how the Sum Multiplexing Gain (SMG) in the network (regardless of the number of users) can be made arbitrarily close to the SMG of a centralized network with an orthogonal scheme such as Time Division (TD). An interesting observation is that in general the elements of the vectors in a signature codeword must not be equiprobable over the underlying alphabet in contrast to the use of binary Pseudo-random Noise (PN) signatures in randomly spread CDMA where the chip elements are +1 or -1 with equal probability. The main reason for this phenomenon is the interplay between two factors appearing in the expression of the achievable rate, i.e., multiplexing gain and the so-called interference entropy factor. In the sequel, invoking an information theoretic extremal inequality, we present an optimality result by showing that in randomized frequency hopping which is the main idea in the prevailing bluetooth devices in decentralized networks, transmission of independent signals in consecutive transmission slots is in general suboptimal regardless of the distribution of the signals. Finally, chapter 4 addresses a decentralized Gaussian interference channel consisting of two block-asynchronous transmitter-receiver pairs. We consider a scenario where the rate of data arrival at the encoders is considerably low and codewords of each user are transmitted at random instants depending on the availability of enough data for transmission. This makes the transmitted signals by each user look like scattered bursts along the time axis. Users are block-asynchronous meaning there exists a delay between their transmitted signal bursts. The proposed model for asynchrony assumes the starting point of an interference burst is uniformly distributed along the transmitted codeword of any user. There is also the possibility that each user does not experience interference on a transmitted codeword at all. Due to the randomness of delay, the channels are non-ergodic in the sense that the transmitters are unaware of the location of interference bursts along their transmitted codewords. In the proposed scheme, upon availability of enough data in its queue, each user follows a locally Randomized Masking (RM) strategy where the transmitter quits transmitting the Gaussian symbols in its codeword independently from symbol interval to symbol interval. An upper bound on the probability of outage per user is developed using entropy power inequality and a key upper bound on the differential entropy of a mixed Gaussian random variable. It is shown that by adopting the RM scheme, the probability of outage is considerably less than the case where both users transmit the Gaussian symbols in their codewords in consecutive symbol intervals, referred to as Continuous Transmission (CT).

abstract: There has been a lot of work on the characterization of capacity and achievable rate regions, and rate region outer-bounds for various multi-user channels of interest. Parallel to the developed information theoretic results, practical codes have also been designed for some multi-user channels such as multiple access channels, broadcast channels and relay channels; however, interference channels have not received much attention and only a limited amount of work has been conducted on them. With this motivation, in this dissertation, design of practical and implementable channel codes is studied focusing on multi-user channels with special emphasis on interference channels; in particular, irregular low-density-parity-check codes are exploited for a variety of cases and trellis based codes for short block length designs are performed. Novel code design approaches are first studied for the two-user Gaussian multiple access channel. Exploiting Gaussian mixture approximation, new methods are proposed wherein the optimized codes are shown to improve upon the available designs and off-the-shelf point-to-point codes applied to the multiple access channel scenario. The code design is then examined for the two-user Gaussian interference channel implementing the Han-Kobayashi encoding and decoding strategy. Compared with the point-to-point codes, the newly designed codes consistently offer better performance. Parallel to this work, code design is explored for the discrete memoryless interference channels wherein the channel inputs and outputs are taken from a finite alphabet and it is demonstrated that the designed codes are superior to the single user codes used with time sharing. Finally, the code design principles are also investigated for the two-user Gaussian interference channel employing trellis-based codes with short block lengths for the case of strong and mixed interference levels. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2015