Optimizing Quantize-Map-and-Forward Relaying for Gaussian Diamond Networks

We evaluate the information-theoretic achievable rates of Quantize-Map-and-Forward (QMF) relaying schemes over Gaussian $N$-relay diamond networks. Focusing on vector Gaussian quantization at the relays, our goal is to understand how close to the cutset upper bound these schemes can achieve in the context of diamond networks, and how much benefit is obtained by optimizing the quantizer distortions at the relays. First, with noise-level quantization, we point out that the worst-case gap from the cutset upper bound is $(N+\log_2 N)$ bits/s/Hz. A better universal quantization level found without using channel state information (CSI) leads to a sharpened gap of $\log_2 N + \log_2(1+N) + N\log_2(1 + 1/N)$ bits/s/Hz. On the other hand, it turns out that finding the optimal distortion levels depending on the channel gains is a non-trivial problem in the general $N$-relay setup. We manage to solve the two-relay problem and the symmetric $N$-relay problem analytically, and show the improvement via numerical evaluations both in static as well as slow-fading channels

On the Achievable Rates of Multihop Virtual Full-Duplex Relay Channels

We study a multihop "virtual" full-duplex relay channel as a special case of a general multiple multicast relay network. For such channel, quantize-map-and-forward (QMF) (or noisy network coding (NNC)) achieves the cut-set upper bound within a constant gap where the gap grows {\em linearly} with the number of relay stages $K$. However, this gap may not be negligible for the systems with multihop transmissions (i.e., a wireless backhaul operating at higher frequencies). We have recently attained an improved result to the capacity scaling where the gap grows {\em logarithmically} as $\log{K}$, by using an optimal quantization at relays and by exploiting relays' messages (decoded in the previous time slot) as side-information. In this paper, we further improve the performance of this network by presenting a mixed scheme where each relay can perform either decode-and-forward (DF) or QMF with possibly rate-splitting. We derive the achievable rate and show that the proposed scheme outperforms the QMF-optimized scheme. Furthermore, we demonstrate that this performance improvement increases with $K$.Comment: To be presented at ISIT 201

Physical Layer Cooperation:Theory and Practice

Information theory has long pointed to the promise of physical layer cooperation in boosting the spectral efficiency of wireless networks. Yet, the optimum relaying strategy to achieve the network capacity has till date remained elusive. Recently however, a relaying strategy termed Quantize-Map-and-Forward (QMF) was proved to achieve the capacity of arbitrary wireless networks within a bounded additive gap. This thesis contributes to the design, analysis and implementation of QMF relaying by optimizing its performance for small relay networks, proposing low-complexity iteratively decodable codes, and carrying out over-the-air experiments using software-radio testbeds to assess real-world potential and competitiveness. The original QMF scheme has each relay performing the same operation, agnostic to the network topology and the channel state information (CSI); this facilitates the analysis for arbitrary networks, yet comes at a performance penalty for small networks and medium SNR regimes. In this thesis, we demonstrate the benefits one can gain for QMF if we optimize its performance by leveraging topological and channel state information. We show that for the N-relay diamond network, by taking into account topological information, we can exponentially reduce the QMF additive approximation gap from $\Theta(N)$ bits/s/Hz to $\Theta(\log N)$ bits/s/Hz, while for the one-relay and two-relay networks, use of topological information and CSI can help to gain as much as $6$ dB. Moreover, we explore what benefits we can realize if we jointly optimize QMF and half-duplex scheduling, as well as if we employ hybrid schemes that combine QMF and Decode-and-Forward (DF) relay operations. To take QMF from being a purely information-theoretic idea to an implementable strategy, we derive a structure employing Low-Density-Parity-Check (LDPC) ensembles for the relay node operations and message-passing algorithms for decoding. We demonstrate through extensive simulation results over the full-duplex diamond network, that our designs offer a robust performance over fading channels and achieves the full diversity order of our network at moderate SNRs. Next, we explore the potential real-world impact of QMF and present the design and experimental evaluation of a wireless system that exploits relaying in the context of WiFi. We deploy three main competing strategies that have been proposed for relaying, Amplify-and-Forward (AF), DF and QMF, on the WarpLab software radio platform. We present experimental results--to the best of our knowledge, the first ones--that compare QMF, AF and DF in a realistic indoor setting. We find that QMF is a competitive scheme to the other two, offering in some cases up to 12% throughput benefits and up to 60% improvement in frame error-rates over the next best scheme. We then present a more advanced architecture for physical layer cooperation (termed QUILT), that seamlessly adapts to the underlying network configuration to achieve competitive or better performance than the best current approaches. It combines on-demand, opportunistic use of DF or QMF followed by interleaving at the relay, with hybrid decoding at the destination that extracts information from even potentially undecodable received frames. We theoretically quantify how our design choices affect the system performance. We also deploy QUILT on WarpLab and show through over-the-air experiments up to $5$ times FER improvement over the next best cooperative protocol

Wireless Network Simplification: the Gaussian N-Relay Diamond Network

We consider the Gaussian N-relay diamond network, where a source wants to communicate to a destination node through a layer of N-relay nodes. We investigate the following question: what fraction of the capacity can we maintain by using only k out of the N available relays? We show that independent of the channel configurations and the operating SNR, we can always find a subset of k relays which alone provide a rate (kC/(k+1))-G, where C is the information theoretic cutset upper bound on the capacity of the whole network and G is a constant that depends only on N and k (logarithmic in N and linear in k). In particular, for k = 1, this means that half of the capacity of any N-relay diamond network can be approximately achieved by routing information over a single relay. We also show that this fraction is tight: there are configurations of the N-relay diamond network where every subset of k relays alone can at most provide approximately a fraction k/(k+1) of the total capacity. These high-capacity k-relay subnetworks can be also discovered efficiently. We propose an algorithm that computes a constant gap approximation to the capacity of the Gaussian N-relay diamond network in O(N log N) running time and discovers a high-capacity k-relay subnetwork in O(kN) running time. This result also provides a new approximation to the capacity of the Gaussian N-relay diamond network which is hybrid in nature: it has both multiplicative and additive gaps. In the intermediate SNR regime, this hybrid approximation is tighter than existing purely additive or purely multiplicative approximations to the capacity of this network.Comment: Submitted to Transactions on Information Theory in October 2012. The new version includes discussions on the algorithmic complexity of discovering a high-capacity subnetwork and on the performance of amplify-and-forwar