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

On the Capacity Region of the Two-user Interference Channel with a Cognitive Relay

This paper considers a variation of the classical two-user interference channel where the communication of two interfering source-destination pairs is aided by an additional node that has a priori knowledge of the messages to be transmitted, which is referred to as the it cognitive relay. For this Interference Channel with a Cognitive Relay (ICCR) In particular, for the class of injective semi-deterministic ICCRs, a sum-rate upper bound is derived for the general memoryless ICCR and further tightened for the Linear Deterministic Approximation (LDA) of the Gaussian noise channel at high SNR, which disregards the noise and focuses on the interaction among the users' signals. The capacity region of the symmetric LDA is completely characterized except for the regime of moderately weak interference and weak links from the CR to the destinations. The insights gained from the analysis of the LDA are then translated back to the symmetric Gaussian noise channel (GICCR). For the symmetric GICCR, an approximate characterization (to within a constant gap) of the capacity region is provided for a parameter regime where capacity was previously unknown. The approximately optimal scheme suggests that message cognition at a relay is beneficial for interference management as it enables simultaneous over the air neutralization of the interference at both destinations

Incremental Relaying for the Gaussian Interference Channel with a Degraded Broadcasting Relay

This paper studies incremental relay strategies for a two-user Gaussian relay-interference channel with an in-band-reception and out-of-band-transmission relay, where the link between the relay and the two receivers is modelled as a degraded broadcast channel. It is shown that generalized hash-and-forward (GHF) can achieve the capacity region of this channel to within a constant number of bits in a certain weak relay regime, where the transmitter-to-relay link gains are not unboundedly stronger than the interference links between the transmitters and the receivers. The GHF relaying strategy is ideally suited for the broadcasting relay because it can be implemented in an incremental fashion, i.e., the relay message to one receiver is a degraded version of the message to the other receiver. A generalized-degree-of-freedom (GDoF) analysis in the high signal-to-noise ratio (SNR) regime reveals that in the symmetric channel setting, each common relay bit can improve the sum rate roughly by either one bit or two bits asymptotically depending on the operating regime, and the rate gain can be interpreted as coming solely from the improvement of the common message rates, or alternatively in the very weak interference regime as solely coming from the rate improvement of the private messages. Further, this paper studies an asymmetric case in which the relay has only a single single link to one of the destinations. It is shown that with only one relay-destination link, the approximate capacity region can be established for a larger regime of channel parameters. Further, from a GDoF point of view, the sum-capacity gain due to the relay can now be thought as coming from either signal relaying only, or interference forwarding only.Comment: To appear in IEEE Trans. on Inf. Theor

Cooperative Strategies for Simultaneous and Broadcast Relay Channels

Consider the \emph{simultaneous relay channel} (SRC) which consists of a set of relay channels where the source wishes to transmit common and private information to each of the destinations. This problem is recognized as being equivalent to that of sending common and private information to several destinations in presence of helper relays where each channel outcome becomes a branch of the \emph{broadcast relay channel} (BRC). Cooperative schemes and capacity region for a set with two memoryless relay channels are investigated. The proposed coding schemes, based on \emph{Decode-and-Forward} (DF) and \emph{Compress-and-Forward} (CF) must be capable of transmitting information simultaneously to all destinations in such set. Depending on the quality of source-to-relay and relay-to-destination channels, inner bounds on the capacity of the general BRC are derived. Three cases of particular interest are considered: cooperation is based on DF strategy for both users --referred to as DF-DF region--, cooperation is based on CF strategy for both users --referred to as CF-CF region--, and cooperation is based on DF strategy for one destination and CF for the other --referred to as DF-CF region--. These results can be seen as a generalization and hence unification of previous works. An outer-bound on the capacity of the general BRC is also derived. Capacity results are obtained for the specific cases of semi-degraded and degraded Gaussian simultaneous relay channels. Rates are evaluated for Gaussian models where the source must guarantee a minimum amount of information to both users while additional information is sent to each of them.Comment: 32 pages, 7 figures, To appear in IEEE Trans. on Information Theor

Generalized Degrees of Freedom of the Interference Channel with a Signal Cognitive Relay

We study the interference channel with a signal cognitive relay. A signal cognitive relay knows the transmit signals (but not the messages) of the sources non-causally, and tries to help them communicating with their respective destinations. We derive upper bounds and provide achievable schemes for this channel. These upper and lower bounds are shown to be tight from generalized degrees of freedom point of view. As a result, a characterization of the generalized degrees of freedom of the interference channel with a signal cognitive relay is given.Comment: Results submitted to ISIT 2010, 19 pages, 3 figure

Nested Lattice Codes for Gaussian Relay Networks with Interference

In this paper, a class of relay networks is considered. We assume that, at a node, outgoing channels to its neighbors are orthogonal, while incoming signals from neighbors can interfere with each other. We are interested in the multicast capacity of these networks. As a subclass, we first focus on Gaussian relay networks with interference and find an achievable rate using a lattice coding scheme. It is shown that there is a constant gap between our achievable rate and the information theoretic cut-set bound. This is similar to the recent result by Avestimehr, Diggavi, and Tse, who showed such an approximate characterization of the capacity of general Gaussian relay networks. However, our achievability uses a structured code instead of a random one. Using the same idea used in the Gaussian case, we also consider linear finite-field symmetric networks with interference and characterize the capacity using a linear coding scheme.Comment: 23 pages, 5 figures, submitted to IEEE Transactions on Information Theor