Compute-and-Forward Relay Networks with Asynchronous, Mobile, and Delay-Sensitive Users

We consider a wireless network consisting of multiple source nodes, a set of relays and a destination node. Suppose the sources transmit their messages simultaneously to the relays and the destination aims to decode all the messages. At the physical layer, a conventional approach would be for the relay to decode the individual message one at a time while treating rest of the messages as interference. Compute-and-forward is a novel strategy which attempts to turn the situation around by treating the interference as a constructive phenomenon. In compute-and-forward, each relay attempts to directly compute a combination of the transmitted messages and then forwards it to the destination. Upon receiving the combinations of messages from the relays, the destination can recover all the messages by solving the received equations. When identical lattice codes are employed at the sources, error correction to integer combination of messages is a viable option by exploiting the algebraic structure of lattice codes. Therefore, compute-and-forward with lattice codes enables the relay to manage interference and perform error correction concurrently. It is shown that compute-and-forward exhibits substantial improvement in the achievable rate compared with other state-of-the-art schemes for medium to high signal-to-noise ratio regime. Despite several results that show the excellent performance of compute-and-forward, there are still important challenges to overcome before we can utilize compute-and- forward in practice. Some important challenges include the assumptions of \perfect timing synchronization "and \quasi-static fading", since these assumptions rarely hold in realistic wireless channels. So far, there are no conclusive answers to whether compute-and-forward can still provide substantial gains even when these assumptions are removed. When lattice codewords are misaligned and mixed up, decoding integer combination of messages is not straightforward since the linearity of lattice codes is generally not invariant to time shift. When channel exhibits time selectivity, it brings challenges to compute-and-forward since the linearity of lattice codes does not suit the time varying nature of the channel. Another challenge comes from the emerging technologies for future 5G communication, e.g., autonomous driving and virtual reality, where low-latency communication with high reliability is necessary. In this regard, powerful short channel codes with reasonable encoding/decoding complexity are indispensable. Although there are fruitful results on designing short channel codes for point-to-point communication, studies on short code design specifically for compute-and-forward are rarely found. The objective of this dissertation is threefold. First, we study compute-and-forward with timing-asynchronous users. Second, we consider the problem of compute-and- forward over block-fading channels. Finally, the problem of compute-and-forward for low-latency communication is studied. Throughout the dissertation, the research methods and proposed remedies will center around the design of lattice codes in order to facilitate the use of compute-and-forward in the presence of these challenges

Applications of Lattices over Wireless Channels

In wireless networks, reliable communication is a challenging issue due to many attenuation factors such as receiver noise, channel fading, interference and asynchronous delays. Lattice coding and decoding provide efficient solutions to many problems in wireless communications and multiuser information theory. The capability in achieving the fundamental limits, together with simple and efficient transmitter and receiver structures, make the lattice strategy a promising approach. This work deals with problems of lattice detection over fading channels and time asynchronism over the lattice-based compute-and-forward protocol. In multiple-input multiple-output (MIMO) systems, the use of lattice reduction significantly improves the performance of approximate detection techniques. In the first part of this thesis, by taking advantage of the temporal correlation of a Rayleigh fading channel, low complexity lattice reduction methods are investigated. We show that updating the reduced lattice basis adaptively with a careful use of previous channel realizations yields a significant saving in complexity with a minimal degradation in performance. Considering high data rate MIMO systems, we then investigate soft-output detection methods. Using the list sphere decoder (LSD) algorithm, an adaptive method is proposed to reduce the complexity of generating the list for evaluating the log-likelihood ratio (LLR) values. In the second part, by applying the lattice coding and decoding schemes over asynchronous networks, we study the impact of asynchronism on the compute-and-forward strategy. While the key idea in compute-and-forward is to decode a linear synchronous combination of transmitted codewords, the distributed relays receive random asynchronous versions of the combinations. Assuming different asynchronous models, we design the receiver structure prior to the decoder of compute-and-forward so that the achievable rates are maximized at any signal-to-noise-ratio (SNR). Finally, we consider symbol-asynchronous X networks with single antenna nodes over time-invariant channels. We exploit the asynchronism among the received signals in order to design the interference alignment scheme. It is shown that the asynchronism provides correlated channel variations which are proved to be sufficient to implement the vector interference alignment over the constant X network