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

Integer-Forcing Linear Receivers

Linear receivers are often used to reduce the implementation complexity of multiple-antenna systems. In a traditional linear receiver architecture, the receive antennas are used to separate out the codewords sent by each transmit antenna, which can then be decoded individually. Although easy to implement, this approach can be highly suboptimal when the channel matrix is near singular. This paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer-valued entries. Rather than attempting to recover transmitted codewords directly, the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix. The codewords are all generated using the same linear code which guarantees that these integer combinations are themselves codewords. Provided that the effective channel is full rank, these integer combinations can then be digitally solved for the original codewords. This paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter(s), which corresponds either to a multi-user uplink scenario or to single-user V-BLAST encoding. In this setting, the proposed integer-forcing linear receiver significantly outperforms conventional linear architectures such as the zero-forcing and linear MMSE receiver. In the high SNR regime, the proposed receiver attains the optimal diversity-multiplexing tradeoff for the standard MIMO channel with no coding across transmit antennas. It is further shown that in an extended MIMO model with interference, the integer-forcing linear receiver achieves the optimal generalized degrees-of-freedom.Comment: 40 pages, 16 figures, to appear in the IEEE Transactions on Information Theor

Capacity Results for Interference Networks and Nested Cut-Set Bound

In this thesis, a full characterization of the sum-rate capacity for degraded interference networks with any number of transmitters, any number of receivers, and any possible distribution of messages among transmitters and receivers is established. It is proved that a successive decoding scheme is sum-rate optimal for these networks. Moreover, it is shown that the transmission of only a certain subset of messages is sufficient to achieve the sum-rate capacity for such networks. Algorithms are presented to determine this subset of messages explicitly. The sum-rate expression for the degraded networks is then used to derive a unified outer bound on the sum-rate capacity of arbitrary (non-degraded) interference networks. Several variations of degraded networks are identified for which the derived outer bound is sum-rate optimal. Specifically, noisy interference regimes are derived for certain classes of multi-user/multi-message large interference networks. Also, network scenarios are identified where the incorporation of both successive decoding and treating interference as noise achieves their sum-rate capacity. Next, by taking insight from the results for degraded networks, an extension to the standard cut-set bound for general communication networks is presented which is referred to as nested cut-set bound. This bound is derived by applying a series of cuts in a nested configuration to the network first and then bounding the information rate that flows through the cuts. The key idea for bounding step is indeed to impose a degraded arrangement among the receivers corresponding to the cuts. Therefore, the bound is in fact a generalization of the outer bound for interference networks: here cooperative relaying nodes are introduced into the problem as well but the proof style for the derivation of the outer bound remains the same. The nested cut-set bound, which uniformly holds for all general communication networks of arbitrary large sizes where any subset of nodes may cooperatively communicate to any other subset of them, is indeed tighter than the cut-set bound for networks with more than one receiver. Moreover, it includes the generalized cut-set bound for deterministic networks reported by Shomorony and Avestimehr which was originally a special case of the outer bound established for the interference networks by the author (2012). Finally, capacity bounds for the two-user interference channel with cooperative receivers via conferencing links of finite capacities are investigated. The capacity results known for this communication scenario are limited to a very few special cases of the one-sided channel. One of the major challenges in analyzing such cooperative networks is how to establish efficient capacity outer iv bounds for them. In this thesis, by applying new techniques, novel capacity outer bounds are presented for the interference channels with conferencing users. Using the outer bounds, several new capacity results are proved for interesting channels with unidirectional cooperation in strong and mixed interference regimes. A fact is that the conferencing link (between receivers) may be utilized to provide one receiver with information about its corresponding signal or its non-corresponding signal (interference signal). As an interesting consequence, it is demonstrated that both strategies can be helpful to achieve the capacity of the channel. Lastly, for the case of Gaussian interference channel with conferencing receivers, it is argued that our outer bound is strictly tighter than the previous one derived by Wang and Tse