Gaussian Two-way Relay Channel with Private Information for the Relay

We introduce a generalized two-way relay channel where two sources exchange information (not necessarily of the same rate) with help from a relay, and each source additionally sends private information to the relay. We consider the Gaussian setting where all point-to-point links are Gaussian channels. For this channel, we consider a two-phase protocol consisting of a multiple access channel (MAC) phase and a broadcast channel (BC) phase. We propose a general decode-and-forward (DF) scheme where the MAC phase is related to computation over MAC, while the BC phase is related to BC with receiver side information. In the MAC phase, we time share a capacity-achieving code for the MAC and a superposition code with a lattice code as its component code. We show that the proposed DF scheme is near optimal for any channel conditions, in that it achieves rates within half bit of the capacity region of the two-phase protocol.Comment: 6 pages, 3 figures, accepted for publication in IEEE Transactions on Communication

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

Interference Channel with a Half-Duplex Out-of-Band Relay

A Gaussian interference channel (IC) aided by a half-duplex relay is considered, in which the relay receives and transmits in an orthogonal band with respect to the IC. The system thus consists of two parallel channels, the IC and the channel over which the relay is active, which is referred to as Out-of-Band Relay Channel (OBRC). The OBRC is operated by separating a multiple access phase from the sources to the relay and a broadcast phase from the relay to the destinations. Conditions under which the optimal operation, in terms of the sum-capacity, entails either signal relaying and/or interference forwarding by the relay are identified. These conditions also assess the optimality of either separable or non-separable transmission over the IC and OBRC. Specifically, the optimality of signal relaying and separable coding is established for scenarios where the relay-to-destination channels set the performance bottleneck with respect to the source-to-relay channels on the OBRC. Optimality of interference forwarding and non-separable operation is also established in special cases.Comment: 5 pages, 5 figures, to appear in Proceedings of IEEE ISIT 201

On the Capacity Region of the Deterministic Y-Channel with Common and Private Messages

In multi user Gaussian relay networks, it is desirable to transmit private information to each user as well as common information to all of them. However, the capacity region of such networks with both kinds of information is not easy to characterize. The prior art used simple linear deterministic models in order to approximate the capacities of these Gaussian networks. This paper discusses the capacity region of the deterministic Y-channel with private and common messages. In this channel, each user aims at delivering two private messages to the other two users in addition to a common message directed towards both of them. As there is no direct link between the users, all messages must pass through an intermediate relay. We present outer-bounds on the rate region using genie aided and cut-set bounds. Then, we develop a greedy scheme to define an achievable region and show that at a certain number of levels at the relay, our achievable region coincides with the upper bound. Finally, we argue that these bounds for this setup are not sufficient to characterize the capacity region.Comment: 4 figures, 7 page

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

Deterministic Capacity of MIMO Relay Networks

The deterministic capacity of a relay network is the capacity of a network when relays are restricted to transmitting \emph{reliable} information, that is, (asymptotically) deterministic function of the source message. In this paper it is shown that the deterministic capacity of a number of MIMO relay networks can be found in the low power regime where \SNR\to0. This is accomplished through deriving single letter upper bounds and finding the limit of these as \SNR\to0. The advantage of this technique is that it overcomes the difficulty of finding optimum distributions for mutual information.Comment: Submitted to IEEE Transactions on Information Theor