Gaussian Interference Channels: Examining the Achievable Rate Region

Interference is assumed to be one of the main barriers to improving the throughput of communication systems. Consequently, interference management plays an integral role in wireless communications. Although the importance of interference has promoted numerous studies on the interference channel, the capacity region of this channel is still unknown. The focus of this thesis is on Gaussian interference channels. The two-user Gaussian Interference Channel (GIC) represents the standard model of a wireless system in which two independent transmitter-receiver pairs share the bandwidth. Three important problems are investigated: the boundary of the best-known achievable rate region, the complexity of sum-rate optimal codes, and the role of causal cooperation in enlarging the achievable rate region. The best-known achievable rate region for the two-user GIC is due to the Han-Kobayashi (HK) scheme. The HK achievable rate region includes the rate regions achieved by all other known schemes. However, mathematical expressions that characterize the HK rate region are complicated and involve a time sharing variable and two arbitrary power splitting variables. Accordingly, the boundary points of the HK rate region, and in particular the maximum HK sum-rate, are not known in general. The second chapter of this thesis studies the sum-rate of the HK scheme with Gaussian inputs, when time sharing is not used. Note that the optimal input distribution is unknown. However, for all cases where the sum-capacity is known, it is achieved by Gaussian inputs. In this thesis, we examine the HK scheme with Gaussian inputs. For the weak interference class, this study fully characterizes the maximum achievable sum-rate and shows that the weak interference class is partitioned into five parts. For each part, the optimal power splitting and the corresponding maximum achievable sum-rate are expressed in closed forms. In the third chapter, we show that the same approach can be adopted to characterize an arbitrary weighted sum-rate. Moreover, when time sharing is used, we expressed the entire boundary in terms of the upper concave envelope of a function. Consequently, the entire boundary of the HK rate region with Gaussian inputs is fully characterized. The decoding complexity of a given coding scheme is of paramount importance in wireless communications. Most coding schemes proposed for the interference channel take advantage of joint decoding to achieve a larger rate region. However, decoding complexity escalates considerably when joint decoding is used. The fourth chapter studies the achievable sum-rate of the two-user GIC when joint decoding is replaced by successive decoding. This achievable sum-rate is known when interference is mixed. However, when interference is strong or weak, it is not well understood. First, this study proves that when interference is strong and transmitters' powers satisfy certain conditions, the sum-capacity can be achieved by successive decoding. Second, when interference is weak, a novel rate-splitting scheme is proposed that does not use joint decoding. It is proved that the difference between the sum-rate of this scheme and that of the HK scheme is bounded. This study sheds light on the structure of sum-rate optimal codes. Causal cooperation among nodes in a communication system is a promising approach to increasing overall system performance. To guarantee causality, delay is inevitable in cooperative communication systems. Traditionally, delay granularity has been limited to one symbol; however, channel delay is in fact governed by channel memory and can be shorter. For example, the delay requirement in Orthogonal Frequency-Division Multiplexing (OFDM), captured in the cyclic prefix, is typically much shorter than the OFDM symbol itself. This perspective is used in the fifth chapter to study the two-user GIC with full-duplex transmitters. Among other results, it is shown that under a mild condition, the maximum multiplexing gain of this channel is in fact two

Perfect Output Feedback in the Two-User Decentralized Interference Channel

In this paper, the $\eta$-Nash equilibrium ($\eta$-NE) region of the two-user Gaussian interference channel (IC) with perfect output feedback is approximated to within $1$ bit/s/Hz and $\eta$ arbitrarily close to $1$ bit/s/Hz. The relevance of the $\eta$-NE region is that it provides the set of rate-pairs that are achievable and stable in the IC when both transmitter-receiver pairs autonomously tune their own transmit-receive configurations seeking an $\eta$-optimal individual transmission rate. Therefore, any rate tuple outside the $\eta$-NE region is not stable as there always exists one link able to increase by at least $\eta$ bits/s/Hz its own transmission rate by updating its own transmit-receive configuration. The main insights that arise from this work are: $(i)$ The $\eta$-NE region achieved with feedback is larger than or equal to the $\eta$-NE region without feedback. More importantly, for each rate pair achievable at an $\eta$-NE without feedback, there exists at least one rate pair achievable at an $\eta$-NE with feedback that is weakly Pareto superior. $(ii)$ There always exists an $\eta$-NE transmit-receive configuration that achieves a rate pair that is at most $1$ bit/s/Hz per user away from the outer bound of the capacity region.Comment: Revised version (Aug. 2015

Capacity Region of Vector Gaussian Interference Channels with Generally Strong Interference

An interference channel is said to have strong interference if for all input distributions, the receivers can fully decode the interference. This definition of strong interference applies to discrete memoryless, scalar and vector Gaussian interference channels. However, there exist vector Gaussian interference channels that may not satisfy the strong interference condition but for which the capacity can still be achieved by jointly decoding the signal and the interference. This kind of interference is called generally strong interference. Sufficient conditions for a vector Gaussian interference channel to have generally strong interference are derived. The sum-rate capacity and the boundary points of the capacity region are also determined.Comment: 50 pages, 11 figures, submitted to IEEE trans. on Information Theor

On Achievable Rates of the Two-user Symmetric Gaussian Interference Channel

We study the Han-Kobayashi (HK) achievable sum rate for the two-user symmetric Gaussian interference channel. We find the optimal power split ratio between the common and private messages (assuming no time-sharing), and derive a closed form expression for the corresponding sum rate. This provides a finer understanding of the achievable HK sum rate, and allows for precise comparisons between this sum rate and that of orthogonal signaling. One surprising finding is that despite the fact that the channel is symmetric, allowing for asymmetric power split ratio at both users (i.e., asymmetric rates) can improve the sum rate significantly. Considering the high SNR regime, we specify the interference channel value above which the sum rate achieved using asymmetric power splitting outperforms the symmetric case.Comment: 7 pages, to appear in Allerton 201

A New Outer Bound and the Noisy-Interference Sum-Rate Capacity for Gaussian Interference Channels

A new outer bound on the capacity region of Gaussian interference channels is developed. The bound combines and improves existing genie-aided methods and is shown to give the sum-rate capacity for noisy interference as defined in this paper. Specifically, it is shown that if the channel coefficients and power constraints satisfy a simple condition then single-user detection at each receiver is sum-rate optimal, i.e., treating the interference as noise incurs no loss in performance. This is the first concrete (finite signal-to-noise ratio) capacity result for the Gaussian interference channel with weak to moderate interference. Furthermore, for certain mixed (weak and strong) interference scenarios, the new outer bounds give a corner point of the capacity region.Comment: 20 pages, 8 figures, submitted to IEEE Trans. Inform. Theory

Capacity Bounds for a Class of Interference Relay Channels

The capacity of a class of Interference Relay Channels (IRC) -the Injective Semideterministic IRC where the relay can only observe one of the sources- is investigated. We first derive a novel outer bound and two inner bounds which are based on a careful use of each of the available cooperative strategies together with the adequate interference decoding technique. The outer bound extends Telatar and Tse's work while the inner bounds contain several known results in the literature as special cases. Our main result is the characterization of the capacity region of the Gaussian class of IRCs studied within a fixed number of bits per dimension -constant gap. The proof relies on the use of the different cooperative strategies in specific SNR regimes due to the complexity of the schemes. As a matter of fact, this issue reveals the complex nature of the Gaussian IRC where the combination of a single coding scheme for the Gaussian relay and interference channel may not lead to a good coding scheme for this problem, even when the focus is only on capacity to within a constant gap over all possible fading statistics.Comment: 23 pages, 6 figures. Submitted to IEEE Transactions on Information Theory (revised version