Approaching Gaussian Relay Network Capacity in the High SNR Regime: End-to-End Lattice Codes

We present a natural and low-complexity technique for achieving the capacity of the Gaussian relay network in the high SNR regime. Specifically, we propose the use of end-to-end structured lattice codes with the amplify-and-forward strategy, where the source uses a nested lattice code to encode the messages and the destination decodes the messages by lattice decoding. All intermediate relays simply amplify and forward the received signals over the network to the destination. We show that the end-to-end lattice-coded amplify-and-forward scheme approaches the capacity of the layered Gaussian relay network in the high SNR regime. Next, we extend our scheme to non-layered Gaussian relay networks under the amplify-and-forward scheme, which can be viewed as a Gaussian intersymbol interference (ISI) channel. Compared with other schemes, our approach is significantly simpler and requires only the end-to-end design of the lattice precoding and decoding. It does not require any knowledge of the network topology or the individual channel gains

Capacity Bounds for Two-Hop Interference Networks

This paper considers a two-hop interference network, where two users transmit independent messages to their respective receivers with the help of two relay nodes. The transmitters do not have direct links to the receivers; instead, two relay nodes serve as intermediaries between the transmitters and receivers. Each hop, one from the transmitters to the relays and the other from the relays to the receivers, is modeled as a Gaussian interference channel, thus the network is essentially a cascade of two interference channels. For this network, achievable symmetric rates for different parameter regimes under decode-and- forward relaying and amplify-and-forward relaying are proposed and the corresponding coding schemes are carefully studied. Numerical results are also provided.Comment: 8 pages, 5 figures, presented in Allerton Conference'0

Communicating over Filter-and-Forward Relay Networks with Channel Output Feedback

Relay networks aid in increasing the rate of communication from source to destination. However, the capacity of even a three-terminal relay channel is an open problem. In this work, we propose a new lower bound for the capacity of the three-terminal relay channel with destination-to-source feedback in the presence of correlated noise. Our lower bound improves on the existing bounds in the literature. We then extend our lower bound to general relay network configurations using an arbitrary number of filter-and-forward relay nodes. Such network configurations are common in many multi-hop communication systems where the intermediate nodes can only perform minimal processing due to limited computational power. Simulation results show that significant improvements in the achievable rate can be obtained through our approach. We next derive a coding strategy (optimized using post processed signal-to-noise ratio as a criterion) for the three-terminal relay channel with noisy channel output feedback for two transmissions. This coding scheme can be used in conjunction with open-loop codes for applications like automatic repeat request (ARQ) or hybrid-ARQ.Comment: 15 pages, 8 figures, to appear in IEEE Transactions on Signal Processin

Towards the Optimal Amplify-and-Forward Cooperative Diversity Scheme

In a slow fading channel, how to find a cooperative diversity scheme that achieves the transmit diversity bound is still an open problem. In fact, all previously proposed amplify-and-forward (AF) and decode-and-forward (DF) schemes do not improve with the number of relays in terms of the diversity multiplexing tradeoff (DMT) for multiplexing gains r higher than 0.5. In this work, we study the class of slotted amplify-and-forward (SAF) schemes. We first establish an upper bound on the DMT for any SAF scheme with an arbitrary number of relays N and number of slots M. Then, we propose a sequential SAF scheme that can exploit the potential diversity gain in the high multiplexing gain regime. More precisely, in certain conditions, the sequential SAF scheme achieves the proposed DMT upper bound which tends to the transmit diversity bound when M goes to infinity. In particular, for the two-relay case, the three-slot sequential SAF scheme achieves the proposed upper bound and outperforms the two-relay non-orthorgonal amplify-and-forward (NAF) scheme of Azarian et al. for multiplexing gains r < 2/3. Numerical results reveal a significant gain of our scheme over the previously proposed AF schemes, especially in high spectral efficiency and large network size regime.Comment: 30 pages, 11 figures, submitted to IEEE trans. IT, revised versio

Recovering Multiplexing Loss Through Successive Relaying Using Repetition Coding

In this paper, a transmission protocol is studied for a two relay wireless network in which simple repetition coding is applied at the relays. Information-theoretic achievable rates for this transmission scheme are given, and a space-time V-BLAST signalling and detection method that can approach them is developed. It is shown through the diversity multiplexing tradeoff analysis that this transmission scheme can recover the multiplexing loss of the half-duplex relay network, while retaining some diversity gain. This scheme is also compared with conventional transmission protocols that exploit only the diversity of the network at the cost of a multiplexing loss. It is shown that the new transmission protocol offers significant performance advantages over conventional protocols, especially when the interference between the two relays is sufficiently strong.Comment: To appear in the IEEE Transactions on Wireless Communication

Amplify-and-Forward in Wireless Relay Networks

A general class of wireless relay networks with a single source-destination pair is considered. Intermediate nodes in the network employ an amplify-and-forward scheme to relay their input signals. In this case the overall input-output channel from the source via the relays to the destination effectively behaves as an intersymbol interference channel with colored noise. Unlike previous work we formulate the problem of the maximum achievable rate in this setting as an optimization problem with no assumption on the network size, topology, and received signal-to-noise ratio. Previous work considered only scenarios wherein relays use all their power to amplify their received signals. We demonstrate that this may not always maximize the maximal achievable rate in amplify-and-forward relay networks. The proposed formulation allows us to not only recover known results on the performance of the amplify-and-forward schemes for some simple relay networks but also characterize the performance of more complex amplify-and-forward relay networks which cannot be addressed in a straightforward manner using existing approaches. Using cut-set arguments, we derive simple upper bounds on the capacity of general wireless relay networks. Through various examples, we show that a large class of amplify-and-forward relay networks can achieve rates within a constant factor of these upper bounds asymptotically in network parameters.Comment: Minor revision: fixed a typo in eqn. reference, changed the formatting. 30 pages, 8 figure