Relay Broadcast Channel Research Articles

Rate Regions for Relay Broadcast Channels

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A partially cooperative relay broadcast channel (RBC) is a three-node network with one source node and two destination nodes (destinations 1 and 2) where destination 1 can act as a relay to assist destination 2. Inner and outer bounds on the capacity region of the discrete memoryless partially cooperative RBC are obtained. When the relay function is disabled, the inner bound reduces to an inner bound on the capacity region of broadcast channels that includes an inner bound of Marton, and Gel'fand and Pinsker. The outer bound reduces to a new outer bound on the capacity region of broadcast channels that generalizes an outer bound of Marton to include a common message, and that generalizes an outer bound of Gel'fand and Pinsker to apply to general discrete memoryless broadcast channels. The proof for the outer bound simplifies the proof of Gel'fand and Pinsker that was based on a recursive approach. Four classes of RBCs are studied in detail. For the partially cooperative RBC with degraded message sets, inner and outer bounds are obtained. For the semideterministic partially cooperative RBC and the orthogonal partially cooperative RBC, the capacity regions are established. For the parallel partially cooperative RBC with unmatched degraded subchannels, the capacity region is established for the case of degraded message sets. The capacity is also established when the source node has only a private message for destination 2, i.e., the channel reduces to a parallel relay channel with unmatched degraded subchannels. </para>

Duality and Rate Optimization for Multiple Access and Broadcast Channels With Amplify-and-Forward Relays

In this paper, we consider multihop multiple access (MAC) and broadcast channels (BC) where communication takes place with the assistance of relays that amplify and forward (AF) their received signals. For a two-hop parallel AF relay MAC, assuming a sum power constraint across all relays we characterize optimal relay amplification factors and the resulting optimal rate regions. We find the maximum sum rate and the maximum rate for each user in closed form and express the optimal rate pair (R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) that maximizes mu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> +mu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> as the solution of a pair of simultaneous equations. We find that the parallel AF relay MAC with total transmit power of the two users P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> +P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> =P and total relay power P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> is the dual of the parallel AF relay BC where the MAC source nodes become the BC destination nodes, the MAC destination node becomes the BC source node, the dual BC source transmit power is P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> and the total transmit power of the AF relays is P. The duality means that the rate region of the AF relay MAC with a sum power constraint P on the transmitters is the same as that of the dual BC. The duality relationship is found to be useful in characterizing the rate region of the AF relay BC as the union of MAC rate regions. The duality is established for distributed multiple antenna AF relay nodes and multiple (more than 2) hops as well.

Cooperative Relay Broadcast Channels

The capacity regions are investigated for two relay broadcast channels (RBCs), where relay links are incorporated into two-user broadcast channels to support user cooperation. In the first channel, the partially cooperative RBC, only one user in the system acts as a relay. An achievable rate region is derived based on the relay using the decode-and-forward scheme. An outer bound on the capacity region is derived and is shown to be tighter than the cut-set bound. For the special case where the partially cooperative RBC is degraded, the achievable rate region is shown to be the capacity region. Two Gaussian cases of the partially cooperative RBC are studied. For the system where the additive white Gaussian noise (AWGN) term at one receiver is a degraded version of the other, which we refer to as the D-AWGN partially cooperative RBC, the capacity region is established. For the system where the AWGN term at one receiver is independent of the other, which we refer to as the AWGN partially cooperative RBC, inner and outer bounds on the capacity region are derived and are shown to be close. Furthermore, it is shown that feedback does not increase the capacity region for the degraded partially cooperative RBC, but that it improves the capacity region for the nondegraded version. In particular, feedback improves the capacity region for the AWGN partially cooperative RBC. In the second channel model being studied in the paper, the fully cooperative RBC, both users can act as relay nodes. All the results for the partially cooperative RBC are correspondingly generalized to the fully cooperative RBC. In particular, capacity regions are established for the degraded and D-AWGN fully cooperative RBCs. The capacity region is also established for the fully cooperative RBC with feedback. It is further shown that the AWGN fully cooperative RBC has a larger achievable rate region than its partially cooperative counterpart. The results illustrate that relaying and user cooperation are powerful techniques for improving the capacity of broadcast channels

Cooperative Strategies and Capacity Theorems for Relay Networks

Coding strategies that exploit node cooperation are developed for relay networks. Two basic schemes are studied: the relays decode-and-forward the source message to the destination, or they compress-and-forward their channel outputs to the destination. The decode-and-forward scheme is a variant of multihopping, but in addition to having the relays successively decode the message, the transmitters cooperate and each receiver uses several or all of its past channel output blocks to decode. For the compress-and-forward scheme, the relays take advantage of the statistical dependence between their channel outputs and the destination's channel output. The strategies are applied to wireless channels, and it is shown that decode-and-forward achieves the ergodic capacity with phase fading if phase information is available only locally, and if the relays are near the source node. The ergodic capacity coincides with the rate of a distributed antenna array with full cooperation even though the transmitting antennas are not colocated. The capacity results generalize broadly, including to multiantenna transmission with Rayleigh fading, single-bounce fading, certain quasi-static fading problems, cases where partial channel knowledge is available at the transmitters, and cases where local user cooperation is permitted. The results further extend to multisource and multidestination networks such as multiaccess and broadcast relay channels.